Log-Gases and Random Matrices (LMS-34)

Log-Gases and Random Matrices (LMS-34)

Volumn , Issue , 2010, Pages

  Forrester, Peter J ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874083594     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (560)

1. A.Y. Abdul-Magd and M.H. Simbel, Wigner surmise for high order level spacing distributions of chaotic systems, Phys. Rev. E 60 (1999), 5371-5374.
2. P.A. Absil, A. Edelman, and P. Koev, On the largest principal angle between random subspaces, Linear Algebra Appl. 414 (2006), 288-294.
3. M. Adler, P.J. Forrester, T. Nagao, and P. van Moerbeke, Classical skew orthogonal polynomials and random matrices, J. Stat. Phys. 99 (2000), 141-170.
4. M. Adler, E. Horozov, and P. van Moerbeke, The Pfaff lattice and skew-orthogonal polynomials, Int. Math. Res. Notices (11) (1999), 569-588.
5. M. Adler and P. van Moerbeke, Matrix integrals, Toda symmetries, Virasora constraints and orthogonal polynomials, Duke Math. Journal 80 (1995), 863-911.
6. M. Adler and P. van Moerbeke, Toda versus Pfaff latice and related polynomials, Duke Math. J. 112 (2002), 1-58.
7. M. Adler and P. van Moerbeke, Recursion relations for unitary integrals, combinatorics and the Toeplitz lattice, Commun. Math. Phys. 237 (2003), 397-440.
8. A.C. Aitken, Determinants and matrices, 9th ed., Oliver and Boyd, Edinburgh & London, 1956.
9. G. Akemann, The complex Laguerre symplectic ensemble of non-Hermitian matrices, Nucl. Phys. B 73 (2005), 253-299.
10. G. Akemann and E. Kanzieper, Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem, J. Stat. Phys. 129 (2007), 1159-1231.
11. T. Akuzawa and M.Wadati, Non-Hermitian random matrices and integrable quantum Hamiltonians, J. Phys. Soc. Japan 65 (1996), 1583-1588.
12. A. Alastuey and B. Jancovici, On the two-dimensional one-component Coulomb plasma, J. Physique 42 (1981), 1-12.
13. James T. Albrecht, C. Chan, and A. Edelman, Sturm sequences and random eigenvalue distributions, Found. Comput. Math. 9 (2009), 461-483.
14. A. Altland and M.R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid compounds, Phys. Rev. B 55 (1997), 1142-1161.
15. Y. Ameur, H. Hedenmalm, and N. Makarov, Fluctuations of eigenvalues of random matrices, arXiv:0807.0375, 2008.
16. G.W. Anderson, A short proof of Selberg's generalized beta formula, Forum Math. 3 (1991), 415-417.
17. G.E. Andrews, R. Askey, and R. Roy, Special functions, Cambridge University Press, New York, 1999.
18. K. Aomoto, The complex Selberg integral, Quart. J. Math. Oxford 38 (1987), 385-399.
19. K. Aomoto, Jacobi polynomials associated with Selberg's integral, SIAM J. Math. Analysis 18 (1987), 545-549.
20. K. Aomoto, 2 conjectural formulae for symmetric A-type Jackson integrals, unpublished, 1994.
21. K. Aomoto and P.J. Forrester, On the Jacobian identity associated with real hyperplane arrangements, Compositio Math. 121 (2000), 263-295.
22. A.I. Aptekarev, A. Branquinho, and W. Van Assche, Multiple orthogonal polynomials for classical weights, Trans. Amer. Math. Soc. 355 (2003), 3887-3914.
23. R. Askey, An excursion in classical mathematics, unpublished, 1986.
24. R. Askey, Integration and computers, Computers in mathematics (D.V. Chudnovsky and R.D. Jenks, eds.), Lecture notes in pure and applied mathematics, vol. 125, CRC Press, Boca Raton, FL, 1990, pp. 35-82.
25. H. Aslaksen, Quaternion determinants, Math. Intell. 18 (1996), 57-65.
26. Z.D. Bai, Circular law, Ann. Prob. 25 (1997), 494-529.
27. J. Baik, Painlevé expressions for LOE, LSE, and interpolating ensembles, Int. Math. Res. Notices (33) (2002), 1739-1789.
28. J. Baik, Riemann-Hilbert problem problems for last passage percolation, Recent developments in integrable systems and Riemann-Hilbert problems (K. McLaughlin and X. Zhou, eds.), Cont.Math., vol. 326, AMS, Providence, RI, 2003, pp. 1-22.
29. J. Baik, G. Ben Arous, and S. Péché, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, Annals of Prob. 33 (2005), 1643-1697.
30. J. Baik, R. Buckingham, and J. DiFranco, Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function, Commun. Math. Phys. 280 (2008), 463-497.
31. J. Baik, P. Deift, and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J.Amer.Math. Soc. 12 (1999), 1119-1178.
32. J. Baik, P. Deift, and E. Strahov, Products and ratios of characteristic polynomials of random Hermitian matrices, J. Math. Phys. 44 (2003), 3657-3670.
33. J. Baik and E.M. Rains, Limiting distributions for a polynuclear growth model with external sources, J. Stat. Phys. 100 (2000), 523-541.
34. J. Baik and E.M. Rains, Algebraic aspects of increasing subsequences, Duke Math. J. 109 (2001), 1-65.
35. J. Baik and E.M. Rains, The asymptotics of monotone subsequences of involutions, Duke Math. J. 109 (2001), 205-281.
36. T.H. Baker and P.J. Forrester, The Calogero-Sutherland model and generalized classical polynomials, Commun. Math. Phys. 188 (1997), 175-216.
37. J. Baik and E.M. Rains, Finite-n fluctuation formulas for random matrices, J. Stat. Phys. 88 (1997), 1371-1386.
38. J. Baik and E.M. Rains, Generalizations of the q-Morris constant term identity, J. Comb. Theory. Ser. A 81 (1998), 69-87.
39. J. Baik and E.M. Rains, Nonsymmetric jack polynomials and integral kernels, Duke Math. J. 95 (1998), 1-50.
40. J. Baik and E.M. Rains, Symmetric Jack polynomials from nonsymmetric theory, Annals Comb. 3 (1999), 159-170.
41. J. Baik and E.M. Rains, Random walks and random fixed point free involutions, J. Phys. A 34 (2001), L381-L390.
42. N.L. Balazs and A. Voros, Chaos on the pseudosphere, Phys. Rep. 143 (1986), 109-240.
43. H.U. Baranger and P.A. Mello, Mesoscopic transport through chaotic cavities: a random S-matrix theory approach, Phys. Rev. Lett. 73 (1994), 142-145.
44. E.W. Barnes, The theory of the G-function, Quart. J. Pure Appl. Math. 31 (1900), 264-313.
45. Y. Baryshnikov, GUEs and queues, Probab. Theory Relat. Fields 119 (2001), 256-274.
46. E. Basor and T. Ehrhardt, Determinant computations for some classes of Toeplitz-Hankel matrices, arXiv:0804.3073, 2008.
47. E.L. Basor, Toeplitz determinants, Fisher-Hartwig symbols, and random matrices, Recent perspectives in random matrix theory and number theory (F. Mezzadri and N.C. Snaith, eds.), London Mathematical Society Lecture Note Series, vol. 322, Cambridge University Press, Cambridge, 2005, pp. 309-336.
48. E.L. Basor and P.J. Forrester, Formulas for the evaluation of Toeplitz determinants with rational generating functions, Math. Nachr. 170 (1994), 5-18.
49. E.L. Basor, C.A. Tracy, and H. Widom, Asymptotics of level spacing distribtions for random matrices, Phys. Rev. Lett. 69 (1992), 5-8.
50. T. Bayes, An essay towards solving a problem in the doctrine of chances, Phil. Trans. Roy. Soc. London 53 (1763), 370-418.
51. C.W.J. Beenakker, Random-matrix theory of mesoscopic fluctuations in conductors and superconductors, Phys. Rev. B 47 (1993), 15763-15775.
52. C.W.J. Beenakker, On the universality of Brezin's and Zee's spectral correlator, Nucl. Phys. B 422 (1994), 515-520.
53. C.W.J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys. 69 (1997), 731-808.
54. C.W.J. Beenakker and B. Rejaei, Random-matrix theory of parametric correlations in the spectra of disordered metals and chaotic billiards, Physica A 203 (1994), 61-90.
55. E.A. Bender, Central and local limit theorems applied to asymptotic enumeration, J. Combin. Theory Ser. A 15 (1973), 91-111.
56. I. Bengtsson and K. Zyczkowski, Geometry of quantum states, Cambridge University Press, Cambridge, 2006.
57. B. Bergersen, D. Boal, and P. Palffy-Muhoray, Equilibrium configurations of particles on the sphere: the case of logarithmic interactions, J. Phys. A 27 (1994), 2579-2586.
58. D. Bernard, M. Gaudin, F.D.M. Haldane, and V. Pasquier, Yang-Baxter equation in long-range interacting systems, J. Phys. A 26 (1993), 5219-5236.
59. D. Bernard and A. LeClair, A classification of non-Hermitian random matrices, Statistical field theories (A. Cappelli and G. Mussardo, eds.), NATO Science Series II, vol. 73, Springer, Berlin, 2002, pp. 207-214.
60. D. Bernard, V. Pasquier, and D. Serban, Exact solution of long-range interacting spin chains with boundaries, Europhs. Lett. 30 (1995), 301-306.
61. B.A. Bernevig and F.D.M. Haldane, Generalized clustering conditions of jack polynomials at negative Jack parameter α, Phys. Rev. B 77 (2008), 184502.
62. M.V. Berry, Riemann's zeta function: a model for quantum chaos?, Quantum Chaos and Statistical Nuclear Physics (T.H. Seligman and H. Nishioka, eds.), Lecture Notes in Physics, vol. 263, Springer, Berlin, 1986, pp. 1-17.
63. M.V. Berry, Some quantum to classical asymptotics, Quantum Chaos (M.J. Giannoni, A. Voros, and J. Zinn-Justin, eds.), Les Houches Lecture Series, vol. 52, North-Holland, Amsterdam, 1991, pp. 251-304.
64. M.V. Berry and J.P. Keating, The Riemann zeros and eigenvalue asymptotics, SIAMRev. 41 (1999), 236-266.
65. M.V. Berry and M. Robnik, Semi-classical level spacings when regular and chaotic orbits coexist, J. Phys. A 17 (1984), 2413-2421.
66. P. Billingsley, Probability and measure, John Wiley, New York, 1979.
67. P. Bleher and X. Di, Correlations between zeros of non-Gaussian random polynomials, Int. Math. Res. Notices 2004 (2004), 2443-2484.
68. P.M. Bleher and A. Kuijlaars, Random matrices with external source and multiple orthogonal polynomials, Int. Math. Res. Notices 2004 (2004), 109-129.
69. E. Bogomolny, Quantum and arithmetic chaos, Frontiers in number theory, physics and geometry I (P. Cartier, B. Julia, P. Moussa, and P. Vanhove, eds.), Springer, Berlin, 2005, pp. 3-106.
70. E. Bogomolny, O. Bohigas, and P. Leboeuf, Distribution of roots of random polynomials, Phys. Rev. Lett. 68 (1992), 2726-2729.
71. E. Bogomolny, O. Bohigas, and P. Leboeuf, Quantum chaotic dynamics and random polynomials, J. Stat. Phys. 85 (1996), 639-679.
72. E. Bogomolny, O. Bohigas, P. Leboeuf, and A.C. Monastra, On the spacing distribution of the Riemann zeros: corrections to the asymptotic result, J. Phys. A 39 (2006), 10743-10754.
73. E.B. Bogomolny and J.P. Keating, Random matrix theory and the Riemann zeros II: n-point correlations, Nonlinearity 9 (1996), 911-935.
74. E.B. Bogomolny and P. Leboeuf, Statistical properties of the zeros of zeta functions-beyond the Riemann case, Nonlinearity 7 (1994), 1155-1167.
75. O. Bohigas, Compound nucleus resonances, random matrices, quantum chaos, Recent perspectives in random matrix theory and number theory (F. Mezzadri and N.C. Snaith, eds.), London Mathematical Society Lecture Note Series, vol. 322, Cambridge University Press, Cambridge, 2005, pp. 147-183.
76. O. Bohigas and M.P. Pato, Missing levels in correlated spectra, Phys. Lett. B 595 (2004), 171-176.
77. G. Boole, On the comparison of transcendents with certain applications to the theory of definite integrals, Philos. Trans. Roy. Soc. 147 (1857), 745-803.
78. F. Bornemann, On the numerical evaluation of Fredholm determinants, arXiv:0804.2543, 2008.
79. F. Bornemann, On the numerical evaluation of distributions in random matrix theory: a review with an invitation to experimental mathematics, arXiv:0904.1581, 2009.
80. A. Borodin, Biorthogonal ensembles, Nucl. Phys. B 536 (1998), 704-732.
81. A. Borodin, Riemann-Hilbert problem and the discrete Bessel kernel, Inter. Math. Res. Notices (9) (2000), 467-494.
82. A. Borodin, Discrete gap probabilities and discrete Painlevé equations, Duke Math. J. 117 (2003), 489-542.
83. A. Borodin and P. Deift, Fredholm determinants, Jimbo-Miwa-Ueno tau-functions and representation theory, Commun. Pur. Appl. Math. 55 (2002), 1160-1230.
84. A. Borodin, P.L. Ferrari,M. Prähoffer, and T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration, J. Stat. Phys. 129 (2006), 1055-1080.
85. A. Borodin and P.J. Forrester, Increasing subsequences and the hard-to-soft transition in matrix ensembles, J.Phys. A 36 (2003), 2963-2981.
86. A. Borodin and A. Okounkov, A Fredholm determinant formula for Toeplitz determinants, Integral Equations Operator Theory 37 (2000), 386-396.
87. A. Borodin and S. Péché, Airy kernel with two sets of parameters in directed percolation and random matrix theory, J. Stat. Phys. 132 (2008), 275-290.
88. A. Borodin and E.M. Rains, Eynard-Mehta theorem, Schur process and their Pfaffian analogs, J. Stat. Phys. 121 (2005), 291-317.
89. A. Borodin and C.D. Sinclair, The Ginibre ensemble of real random matrices and its scaling limit, arXiv:0805.2986.
90. A. Borodin and A. Soshnikov, Janossy densities I. Determinantal ensembles, J. Stat. Phys. 113 (2003), 595-610.
91. A. Borodin and E. Strahov, Averages of characteristic polynomials in random matrix theory, Commun. Pure Appl. Math. 59 (2004), 161-253.
92. A. Böttcher, On the determinant formula by Borodin, Okounkov, Baik, Deift and Rains, Operator Theory: Advances and Applications 135 (2002), 91-99.
93. P. Bourgade, A. Nikeghbali, and A. Rouault, Circular Jacobi ensembles and deformed Verblunsky coefficients.
94. C. Boutillier, The bead model and limit behaviors of dimer models, Ann. Prob. 37 (2009), 107-142.
95. E. Brézin and S. Hikami, Level spacing of random matrices in an external source, Phys. Rev. E 58 (1998), 7176-7185.
96. E. Brézin and S. Hikami, Characteristic polynomials of random matrices, Commun. Math. Phys. 214 (2000), 111-135.
97. E. Brézin and S. Hikami, Characteristic polynomials of real symmetric random matrices, Commun. Math. Phys. 223 (2001), 363-382.
98. E. Brézin, C. Itzykson, G. Parisi, and J.B. Zuber, Planar diagrams, Commun. Math. Phys. 59 (1978), 35-51.
99. E. Brézin and A. Zee, Universality of the correlations between eigenvalues of large random matrices, Nucl. Phys. B 402 (1993), 613-627.
100. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, and S.S.M. Wong, Random matrix theory, Rev. Mod. Phys. 53 (1981), 329-351.
101. P.W. Brouwer, Generalized circular ensemble of scattering matrices for a chaotic cavity with nonideal leads, Phys. Rev. B 51 (1995), 16878-16884.
102. P.W. Brouwer, K. Frahm, and C.W.J. Beenakker, Quantum mechanical time-delay matrix in chaotic scattering, Phys. Rev. Lett. 78 (1997), 4737-4740.
103. Z. Burda, R.A. Janik, and B. Waclaw, Spectrum of the product of independent random Gaussian matrices, arXiv:0912.3422, 2009.
104. J.M. Caillol, Exact results for a two-dimensional one-component plasma on a sphere, J. Phys. Lett. (Paris) 42 (1981), L245-L247.
105. F. Calogero, Solution of the three-body problem in one dimension, J. Math. Phys. 10 (1969), 2191-2196.
106. J. Cardy, Stochastic Loewner evolution and Dyson's circular ensembles, J. Phys. A 36 (2003), L379-L386.
107. Y. Chen, M.E.H. Ismail, and K.A. Muttalib, A solvable random matrix model for disordered conductors, J. Phys. Cond. Matter 4 (1992), L417-L413.
108. I.V. Cherednik, Double affine Hecke algebras and Macdonald's conjectures, Ann. Math. 141 (1995), 191-216.
109. Ph. Choquard, P. Favre, and Ch. Gruber, On the equation of state of classical one-component systems with longrange forces, J. Stat. Phys. 23 (1980), 405-442.
110. Ph. Choquard, B. Piller, and R. Rentsch, On the dielectric susceptibility of classical Coulomb systems II, J. Stat.Phys. 46 (1987), 599-633.
111. A.J. Chorin, Vorticity and turbulence, Applied Mathematical Sciences, vol. 103, Springer, New York, 1994, pp. 407-424.
112. C. Cohen-Tannoudji, B. Diu, and F. Lalöe, Quantum mechanics, Wiley, Paris, 1977.
113. B. Collins, Product of random projections, Jacobi ensembles and universality problems arising from free probability, Prob. Theory Related Fields 133 (2005), 315-344.
114. B. Collins and P. Sniady, Integration with respect to Haar measure on unitary, orthogonal and symplectic groups, Commun. Math. Phys. 264 (2006), 773-795.
115. J.B. Conrey, Notes on l-functions and random matrices, Frontiers in number theory, physics and geometry I (P. Cartier, B. Julia, P. Moussa, and P. Vanhove, eds.), Springer, Berlin, 2006, pp. 107-162.
116. J.B. Conrey, P.J. Forrester, and N.C. Snaith, Averages of ratios of characteristic polynomials for the compact classical groups, Int. Math. Res. Notices 2005 (2005), 397-431.
117. J.B. Conrey, M.O. Rubinstein, and N.C. Snaith, Moments of the derivative of characteristic polynomials with an application to the Riemann zeta function, Commun. Math. Phys. 267 (2006), 611-629.
118. A.G. Constantine, Some noncentral distribution problems in multivariate analysis, Ann. Math. Statist. 34 (1963), 1270-1285.
119. C.M. Cosgrove, Chazy classes IX-XI of third-order differential equations, Stud. in Appl. Math. 104 (2000), 171-228.
120. C.M. Cosgrove and G. Scoufis, Painlevé classification of a class of differential equations of the second order and second degree, Stud. in Appl. Math. 88 (1993), 25-87.
121. O. Costin and J.L. Lebowitz, Gaussian fluctuations in random matrices, Phys. Rev. Lett. 75 (1995), 69-72.
122. A.W. Davis, On the marginal distributions of the latent roots of the multivariable beta matrix, Ann. Math. Statist. 43 (1972), 1664-1669.
123. N.G. de Bruijn, On some multiple integrals involving determinants, J. Indian Math. Soc. 19 (1955), 133-151.
124. D.S. Dean and S.N. Majumdar, Extreme value statistics of eigenvalues of Gaussian random matrices, Phys. Rev. E 77 (2008), 041108.
125. P. Deift and D. Gioev, Universality in random matrix theory for orthogonal and symplectic ensembles, Int. Math. Res. Papers 2007 (2007), 004-116.
126. P. Deift, A. Its, and I. Krasovsky, Asymptotics of Airy kernel determinant, Commun. Math. Phys. 278 (2008), 643-678.
127. P. Deift, A. Its, I. Krasovsky, and X. Zhou, The Widom-Dyson constant for the gap probability in random matrix theory, J. Comp. Applied Math. 202 (2006), 26-47.
128. P.A. Deift, Application of a commutation formula, Duke Math. J. 45 (1978), 267-310.
129. P.A. Deift, A.R. Its, and X. Zhou, A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrices and also in the theory of integrable statistical mechanics, Ann. Math. 146 (1997), 149-235.
130. A.P. Dempster, Elements of continuous multivariate analysis, Addison-Wesley, Reading, MA, 1969.
131. P. Desrosiers, Duality in random matrix ensembles for all β, Nucl. Phys. B 817 (2009), 224-251.
132. P. Desrosiers and P.J. Forrester, Hermite and Laguerre β-ensembles: asymptotic corrections to the eigenvalue density, Nucl. Phys. B 743 (2006), 307-332.
133. P. Diaconis, Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem, Bull. Amer. Math. Soc. 36 (1999), 413-432.
134. P. Diaconis and M. Shahshahani, The subgroup algorithm for generating uniform random variables, Prob. Eng. Inf. Sci. 1 (1987), 15-32.
135. M. Dieng, Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlevé representations, Int. Math. Res. Notices 2005 (2005), 2263-2287.
136. R.B. Dingle, Asymptotic expansions, Academic Press, New York, 1973.
137. A.L. Dixon, Generalizations of Legendre's formula ké-(k-e)ḱ = 1 2π, Proc. London Math. Soc. 3 (1905), 206-224.
138. V.S. Dotsenko and V.A. Fateev, Four-point correlation functions and the operator algebra in 2D conformal invariant theories with central charge C ≤ 1, Nucl. Phys. B 251 (1985), 691-734.
139. E. Duẽnez, Random matrix ensembles associated to compact symmetric spaces, Ph.D. thesis, Princeton University, 2001.
140. I. Dumitriu and A. Edelman, Matrix models for beta ensembles, J. Math. Phys. 43 (2002), 5830-5847.
141. C.F. Dunkl, Difference-differential operators associated to reflection groups, Trans. Amer.Math. Soc. 311 (1989), 167-183.
142. C.F. Dunkl, Integral kernels with reflection group invariance, Can. J. Math. 43 (1991), 1213-1227.
143. C.F. Dunkl, Hankel transforms associated to finite reflection groups, Contemp. Math. 138 (1992), 123-128.
144. C.F. Dunkl and Y. Xu, Orthogonal polynomials of several variables, Cambridge University Press, Cambridge, 2001.
145. F.J. Dyson, A Brownian motion model for the eigenvalues of a random matrix, J.Math. Phys. 3 (1962), 1191-1198.
146. F.J. Dyson, Statistical theory of energy levels of complex systems I, J. Math. Phys. 3 (1962), 140-156.
147. F.J. Dyson, Statistical theory of energy levels of complex systems II, J. Math. Phys. 3 (1962), 157-165.
148. F.J. Dyson, Statistical theory of energy levels of complex systems III, J. Math. Phys. 3 (1962), 166-175.
149. F.J. Dyson, The three fold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics, J. Math. Phys. 3 (1962), 1199-1215.
150. F.J. Dyson, Correlations between the eigenvalues of a random matrix, Commun. Math. Phys. 19 (1970), 235-250.
151. F.J. Dyson, Quaternion determinants, Helv. Phys. Acta 45 (1972), 289-302.
152. F.J. Dyson, The Coulomb fluid and the fifth Painlevé transcendent, Chen Ning Yang (S.-T. Yau, ed.), International Press, Cambridge MA, 1995, p. 131.
153. F.J. Dyson and M.L. Mehta, Statistical theory of the energy levels of complex systems. IV, J. Math. Phys. 4 (1963), 701-712.
154. A. Edelman, Eigenvalues and condition numbers of random matrices, SIAM J. Matrix Anal. Appl. 9 (1988), 543-560.
155. F.J. Dyson, The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law, J. Multivariate. Anal. 60 (1997), 203-232.
156. A. Edelman, E. Kostlan, and M. Shub, How many eigenvalues of random matrix are real?, J. Amer. Math. Soc. 7 (1994), 247-267.
157. A. Edelman and N. Raj Rao, Random matrix theory, Acta Numerica (A. Iserles, ed.), vol. 14, Cambridge University Press, Cambridge, 2005.
158. A. Edelman and B.D. Sutton, From random matrices to stochastic operators, J. Stat. Phys. 127 (2006), 1121-1165.
159. A. Edelman and B.D. Sutton, The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems, Found. Comput. Math. 8 (2008), 259-285.
160. K.B. Efetov, Supersymmetry and theory of disordered metals, Adv. Phys. 32 (1983), 53-127.
161. K.B. Efetov, Supersymmetry in disorder and chaos, Cambridge University Press, Cambridge, 1997.
162. T. Ehrardt, The asymptotics a Bessel kernel determinant which arises in random matrix theory, arXiv:1001.2340, 2010.
163. T. Ehrhardt, Dyson's constant in the asymptotics of the Fredholm determinant of the sine kernel, Commun. Math. Phys. 262 (2006), 317-341.
164. N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating sign matrices and domino tilings I, J. Algebraic Combin. 1 (1992), 111-132.
165. A. Erdélyi et al.(ed.), Higher transcendental functions, vol. 1and 2, McGraw-Hill, New York, 1953.
166. R. J. Evans, Multidimensional beta and gamma integrals, Contemp. Math. 166 (1994), 341-357.
167. B. Eynard, Asymptotics of skew-orthogonal polynomials, J. Phys. A 34 (2001), 7591-7605.
168. B. Eynard and M.L. Mehta, Matrices coupled in a chain. I. Eigenvalue correlations, J. Phys. A 31 (1998), 4449-4456.
169. E. Faleiro, J.M.G. Gomez, R.A. Molina, A. Relano, and J. Retamosa, Theoretical derivation of 1/f noise in quantum chaos, Phys. Rev. Lett. 93 (2004), 244101.
170. D.W. Farmer, F.Mezzadri, and N.C. Snaith, Random polynomials, random matrices and L-functions, Nonlinearity 19 (2006), 919-936.
171. B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin, A differential ideal of symmetric polynomials spanned by Jack polynomials at β =-(r-1)/(k +1), Int. Math. Res. Not. no. 23 (2002), 1223-1237.
172. J. Feinberg and A. Zee, Non-Hermitean random matrix theory: method of Hermitian reduction, Nucl. Phys. B 504 (1997), 579-608.
173. P.L. Ferrari and H. Spohn, A determinantal formula for the GOE Tracy Widom distribution, J. Phys. A 38 (2005), L557-L561.
174. R.P. Feynman, Forces in molecules, Phys. Rev. 56 (1939), 340-343.
175. M.E. Fisher, Walks, walls, wetting, and melting, J. Stat. Phys. 34 (1984), 667-729.
176. M.E. Fisher and R.E. Hartwig, Toeplitz determinants-some applications, theorems and conjectures, Adv. Chem. Phys. 15 (1968), 333-353.
177. B.J. Fleming, P.J. Forrester, and E. Nordenstam, A finitization of the bead process, arXiv:0902.0709, 2009.
178. M. Fogler and B.I. Shklovskii, The probability of an eigenvalue fluctuation in an interval of a random matrix spectrum, Phys. Rev. Lett. 74 (1995), 3312-3315.
179. P.J. Forrester, An exactly solvable two-component classical Coulomb system, J. Aust. Math. Soc. Series B 26 (1984), 119-128.
180. P.J. Forrester, Exact results for correlations in a two-component log-gas, J. Stat. Phys. 59 (1989), 57-79.
181. P.J. Forrester, Exact solution of the lockstep model of vicious walkers, J. Phys. A 23 (1990), 1259-1273.
182. P.J. Forrester, Theta function generalizations of some constant term identities in the theory of random matrices, SIAM J. Math. Anal. 21 (1990), 270-280.
183. P.J. Forrester, Exact results for vicious walker models of domain walls, J. Phys. A24 (1991), 203-218.
184. P.J. Forrester, A constant term identity and its relationship to the log-gas and some quantum many body systems, Phys. Lett. A 163 (1992), 121-126.
185. P.J. Forrester, Selberg correlation integrals and the 1/r2 quantum many body system, Nucl. Phys. B 388 (1992), 671-699.
186. P.J. Forrester, Some statistical properties of the eigenvalues of complex random matrices, Phys. Lett. A 169 (1992), 21-24.
187. P.J. Forrester, Exact results and universal asymptotics in the Laguerre random matrix ensemble, J. Math. Phys. 35 (1993), 2539-2551.
188. P.J. Forrester, Recurrence equations for the computation of correlations in the 1/r2 quantum many body system, J. Stat. Phys. 72 (1993), 39-50.
189. P.J. Forrester, The spectrum edge of random matrix ensembles, Nucl. Phys. B 402 (1993), 709-728.
190. P.J. Forrester, Addendum to Selberg correlation integrals and the 1/r2 quantum many body system, Nucl. Phys. B 416 (1994), 377-385.
191. P.J. Forrester, Properties of an exact crystalline many-body ground state, J. Stat. Phys. 76 (1994), 331-346.
192. P.J. Forrester, Integration formulas and exact calculations in the Calogero-Sutherland model, Mod. Phys. Lett B 9 (1995), 359-371.
193. P.J. Forrester, Normalization of the wave function for the Calogero-Sutherland model with internal degrees of freedom, Int. J. Mod. Phys. B 9 (1995), 1243-1261.
194. P.J. Forrester, Fluctuation formula for complex random matrices, J. Phys. A 32 (1999), L159-L163.
195. P.J. Forrester, Painlevé transcendent evaluation of the scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles, nlin.SI/0005064, 2000.
196. P.J. Forrester, Growth models, random matrices and Painlevé transcendents, Nonlinearity 16 (2003), R27-R49.
197. P.J. Forrester, Evenness symmetry and inter-relationships between gap probabilities in random matrix theory, Forum Math. 18 (2006), 711-743.
198. P.J. Forrester, Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry, Nonlinearity 19 (2006), 2989-3002.
199. P.J. Forrester, A random matrix decimation procedure relating β = 2/(r +1) to β = 2(r +1), Commun. Math. Phys. 285 (2007), 653-672.
200. P.J. Forrester, Beta random matrix ensembles, Random matrix theory and its applications (Z. Bai, Y. Chen, and Y.-C. Liang, eds.), Lecture Notes Series, IMS, NUS, vol. 18, World Scientific, Singapore, 2009, pp. 27-68.
201. P.J. Forrester and N.E. Frankel, Applications and generalizations of Fisher-Hartwig asymptotics, J. Math. Phys. 45 (2003), 2003-2028.
202. P.J. Forrester, N.E. Frankel, and T.M. Garoni, Asymptotic form of the density profile for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry, J. Math. Phys. 47 (2006), 023301.
203. P.J. Forrester and G. Honner, Exact statistical properties of the zeros of complex random polynomials, J. Phys. A 32 (1999), 7.
204. P.J. Forrester and T.D. Hughes, Complex Wishart matrices and conductance in mesoscopic systems: exact results, J. Math. Phys. 35 (1994), 6736-6747.
205. P.J. Forrester and B. Jancovici, Two-dimensional one-component plasma in a quadrupolar field, Int. J. Mod. Phys. A 11 (1996), 941-949.
206. P.J. Forrester and B. Jancovici, Exact and asymptotic formulas for overdamped Brownian dynamics, Physica A 238 (1997), 7.
207. P.J. Forrester, B. Jancovici, and D.S. McAnally, Analytic properties of the structure function for the onedimensional one-component log-gas, J. Stat. Phys. 102 (2000), 737-780.
208. P.J. Forrester, B. Jancovici, and G. Téllez, Universality in some classical Coulomb systems of restricted domain, J. Stat. Phys. 84 (1996), 359-378.
209. P.J. Forrester and M. Krishnapur, Derivation of an eigenvalue probability density function relating to the Poincar é disk, J. Phys. A 42 (2009), 385204 (10pp).
210. P.J. Forrester and A. Mays, A method to calculate correlation functions for β = 1 random matrices of odd size, J. Stat. Phys. 134 (2009), 7.
211. P.J. Forrester, D.S. McAnally, and Y. Nikoyalevsky, On the evaluation formula for Jack polynomials with prescribed symmetry, J. Phys. A 34 (2001), 8407-8424.
212. P.J. Forrester and T. Nagao, Correlations for the circular Dyson Brownian motion model with Poisson initial conditions, Nucl. Phys. B 532 (1998), 733-752.
213. P.J. Forrester and T. Nagao, Correlations for the Cauchy and generalized circular ensembles with orthogonal and symplectic symmetry, J. Phys. A 34 (2001), 7917-7932.
214. P.J. Forrester and T. Nagao, Eigenvalue statistics of the real Ginibre ensemble, Phys. Rev. Lett. 99 (2007), 050603.
215. P.J. Forrester and T. Nagao, Determinantal correlations for classical projection processes, arXiv:0801.0100, 2008.
216. P.J. Forrester, T. Nagao, and G. Honner, Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges, Nucl. Phys. B 553 (1999), 601-643.
217. P.J. Forrester, T. Nagao, and E.M. Rains, Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges, Int. Math. Res. Notices 2006 (2006), 89796 (35 pages).
218. P.J. Forrester and A.M. Odlyzko, Gaussian unitary ensemble eigenvalues and Riemann ζ function zeros: a nonlinear equation for a new statistic, Phys. Rev. E 54 (1996), R4493-R4495.
219. P.J. Forrester and C. Pisani, The hole probability in log-gas and random matrix systems, Nucl. Phys. B 374 (1992), 720-740.
220. P.J. Forrester and E.M. Rains, Inter-relationships between orthogonal, unitary and symplectic matrix ensembles, Random matrix models and their applications (P.M. Bleher and A.R. Its, eds.), Mathematical Sciences Research Institute Publications, vol. 40, Cambridge University Press, Cambridge, 2001, pp. 171-208.
221. P.J. Forrester and E.M. Rains, Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter, Prob. Theory Related Fields 130 (2004), 518-576.
222. P.J. Forrester and E.M. Rains, Interpretations of some parameter dependent generalizations of classical matrix ensembles, Prob. Theory Related Fields 131 (2005), 1-61.
223. P.J. Forrester and E.M. Rains, Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices, Int. Math. Res. Not. 2006 (2006), 48306 (36 pages).
224. P.J. Forrester and E.M. Rains, Symmetrized models of last passage percolation and non-intersecting lattice paths, J. Stat. Phys. 2007 (2007), 7.
225. P.J. Forrester and J.B. Rogers, Electrostatics and the zeros of the classical polynomials, SIAM J. Math. Anal. 17 (1986), 461-468.
226. P.J. Forrester, N.S. Snaith, and J.J.M. Verbaarschot, Developments in random matrix theory, J. Phys. A 36 (2003), R1-R10.
227. P.J. Forrester and S.O.Warnaar, The importance of the Selberg integral, Bull. Am.Math. Soc. 45 (2008), 489-534.
228. P.J. Forrester and N.S.Witte, Application of the τ-function theory of Painlevé equations to random matrices: PIV, PII and the GUE, Commun. Math. Phys. 219 (2000), 357-398.
229. P.J. Forrester and N.S.Witte, Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles, Lett. Math. Phys. 53 (2000), 195-200.
230. P.J. Forrester and N.S.Witte, Application of the τ-function theory of Painlevé equations to random matrices: PV, PIII, the LUE, JUE and CUE, Commun. Pure Appl. Math. 55 (2002), 679-727.
231. P.J. Forrester and N.S.Witte, τ-function evaluation of gap probabilities in orthogonal and symplectic matrix ensembles, Nonlinearity 15 (2002), 937-954.
232. P.J. Forrester and N.S.Witte, Discrete Painlevé equations and random matrix averages, Nonlinearity 16 (2003), 1919-1944.
233. P.J. Forrester and N.S.Witte, Application of the τ-function theory of Painlevé equations to random matrices: PVI, the JUE,CyUE, cJUE and scaled limits, Nagoya Math. J. 174 (2004), 29-114.
234. P.J. Forrester and N.S.Witte, Discrete Painlevé equations, orthogonal polynomials on the unit circle and n-recurrences for averages over U(N)-PIIÍ and PV τ-functions, Int. Math. Res. Not. (4) (2004), 159-183.
235. P.J. Forrester and N.S.Witte, Boundary conditions associated with the Painlevé IIÍ and V evaluations of some random matrix averages, J. Phys. A 39 (2006), 7.
236. P.J. Forrester and N.S.Witte, Discrete Painlevé equations for a class of PVI τ-functions given as U(N) averages, Nonlinearity 16 (2006), 1919-1944.
237. P.J. Forrester and J.A. Zuk, Applications of the Dotsenko-Fateev integral in random-matrix models, Nucl. Phys. B 473 (1996), 616-630.
238. K. Frahm and J.L. Pichard, Brownian motion ensembles and parametric correlations of the transmission eigenvalues: applications to coupled quantum billiards and to disordered systems, J. Phys. I (France) 5 (1995), 877-906.
239. P. Di Francesco, Matrix model combinatorics: applications to folding and coloring, Random matrix models and their applications (P.M. Bleher and A.R. Its, eds.), Mathematical Sciences Research Institute Publications, vol. 40, Cambridge University Press, Cambridge, 2001, pp. 111-170.
240. P. Di Francesco, Rectangular matrix models and combinatorics of colored graphs, Nucl. Phys. B 648 (2003), 461-496.
241. P. Di Francesco, 2d quantum gravity, matrix models and graph combinatorics, Applications of random matrices to physics (E. Brezin et al., ed.), Springer, Dordrecht, 2006, pp. 33-88.
242. P. Di Francesco, M. Gaudin, C. Itzykson, and F. Lesage, Laughlin's wave functions, Coulomb gases and expansions of the discriminant, Int. J. Mod. Phys. A 9 (1994), 7.
243. J.B. French, P.A.Mello, and A. Pandey, Statistical properties of many-particle spectra. II. Two-point correlations and fluctuations, Ann. Phys. 113 (1978), 277-293.
244. G. Freud, On the coefficients in the recursion formulas of orthogonal polynomials, Proc. Roy. Irish Acad. Sect. A 76 (1976), 1-6.
245. W.H.J. Fuchs, On the eigenvalues of an integral equation arising in the theory of band-limited signals, J.Math. Anal. Appl. 9 (1964), 7.
246. W. Fulton, Young tableaux, London Mathematical Society Student Texts, CUP, Cambridge, 1997.
247. Y.V. Fyodorov, Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation, Nucl. Phys. B 621 (2002), 643-674.
248. Y.V. Fyodorov, Complexity of random energy landscapes, glass transition and absolute value of spectral determinant of random matrices, Phys. Rev. Lett. 92 (2004), 240601, Erratum: Phys. Rev. Lett. 93 (2004), 149901.
249. Y.V. Fyodorov and B.A. Khoruzhenko, On absolute moments of characteristic polynomials of a certain class of complex random matrices, Comm. Math. Phys. 273 (2007), 561-599.
250. Y.V. Fyodorov, B.A. Khoruzhenko, and H.-J. Sommers, Almost-Hermitian random matrices: crossover from Wigner-Dyson to Ginibre eigenvalue statistics, Phys. Rev. Lett. 79 (1997), 557-560.
251. Y.V. Fyodorov and H.-J. Sommers, Universality of "level curvature" distribution for large random matrices: systematic analytical approaches, Zeit. für Phys. B 99 (1995), 7.
252. Y.V. Fyodorov and H.-J. Sommers, Random matrices close to hermitian or unitary: overview of methods and results, J. Phys. A 36 (2003), 3303-3347.
253. G. Gallavoti and C. Marchiori, On the calculation of an integral, J. Math. Ann. Appl. 44 (1973), 661-675.
254. B. Gambier, Sur les équations différentielles du second ordre et du premier degré dont l'intégral gén érale est a points critiques fixes, Acta Math. 33 (1909), 1-55.
255. F.R. Gantmacher, Matrix theory, 2nd ed., Springer, Berlin, 1986.
256. H. Gao and P.J. Smith, A determinant representation for the distribution of quadratic forms in complex normal vectors, J. Multivariate. Anal. 73 (2000), 155-165.
257. T.M. Garoni, Unpublished notes, 2003.
258. T.M. Garoni, P.J. Forrester, and N.E. Frankel, Asymptotic corrections to the eigenvalue density of the GUE and LUE, J. Math. Phys. 46 (2005), 103301.
259. M. Gaudin, Sur la loi limite de l'espacement des valeurs propres d'une matrice al éatoire, Nucl. Phys. 25 (1961), 7.
260. J.S. Geronimo and K.M. Case, Scattering theory and polynomials orthogonal on the unit circle, J. Math. Phys. 20 (1979), 299-310.
261. Ya.L. Geronimus, Orthogonal polynomials, Consultants Bureau, New York, 1961.
262. I.M. Gessel, Symmetric functions and p-recursiveness, J. Comb. Th. A53 (1990), 257-285.
263. S. Ghosh, Skew-orthogonal polynomials and random matrix theory, CRM Monograph Series, vol. 28, American Mathematical Society, Providence, RI, 2009.
264. J. Ginibre, Statistical ensembles of complex, quaternion, and real matrices, J. Math. Phys. 6 (1965), 440-449.
265. V. Girko, Circular law, Th. Prob. Appl. 29 (1984), 694-706.
266. V. Girko, An introduction to statistical analysis of random arrays, Walter de Gruyter, 1998.
267. P. Glynn and W. Whitt, Departures form many queues in series, Ann. Appl. Probability 1 (1991), 546-572.
268. I.J. Good, Short proof of a conjecture of Dyson, J. Math. Phys. 11 (1972), 1884.
269. N.R. Goodman, Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction), Ann. Math. Stat. 34 (1963), 152-176.
270. I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, 4th ed., Academic Press, New York, 1980.
271. W.B.Gragg, Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle, J. Comput. Appl. Math. 46 (1993), 183-198.
272. J. Gravner, C.A. Tracy, and H.Widom, Limit theorems for height fluctuations in a class of discrete space and time fluctuations, J. Stat. Phys. (2001), 1085-1132.
273. C. Greene, An extension of Schensted's theorem, Adv. inMath. 14 (1974), 7.
274. U. Grenander, Probabilites on algebraic structures, John Wiley and Sons, New York, 1963.
275. R. Grobe, F. Haake, and H.-J. Sommers, Quantum distinction of regular chaotic dissipative motion, Phys. Rev. Lett. 61 (1988), 1899-1902.
276. T. Guhr, A. Müller-Groeling, and H.A. Weidenmüller, Random matrix theories in quantum physics: common concepts, Phys. Rep. 299 (1998), 189-425.
277. T. Guhr and T. Wettig, An Itzykson-Zuber like integral and diffusion for complex ordinary and supermatrices, J. Math. Phys. 37 (1996), 6395-6413.
278. J. Gunson, Proof of a conjecture of Dyson in the statistical theory of energy levels, J. Math. Phys. 4 (1962), 752-753.
279. A.K. Gupta and D.K. Nagar, Matrix variate distributions, Chapman & Hall/CRC, Boca Raton, FL, 1999.
280. R.J. Gustafson, A generalization of the Selberg beta-integral, Bull. Am. Math. Soc. 22 (1990), 97-105.
281. J. Gustavsson, Gaussian fluctuations in the GUE, Ann. l'Inst. Henri Poincar é (B) 41 (2005), 151-178.
282. A.J. Guttmann, A.L. Owczarek, and X.G. Viennot, Vicious walkers and Young tableaux I: without walls, J. Phys. A 31 (1998), 8123-8135.
283. Z.N.C. Ha, Fractional statistics in one dimension: view from an exactly solvable model, Nucl. Phys. B 435 (1995), 604-636.
284. F. Haake, Quantum signatures of chaos, 2nd ed., Springer, Berlin, 2000.
285. M. Hallnäs and E. Langmann, Quantum Calogero-Sutherland type models and generalized classical polynomials, arXiv:math-ph/0703090, 2007.
286. J.M. Hammersley, The zeros of random polynomials, Proceedings of the Third Berkeley Symposium on Probability and Statistics (J. Neyman, ed.), vol. 2, Univ. California Press, Berekeley, CA, 1956, pp. 89-111.
287. P.J. Hanlon, R.P. Stanley, and J.R. Stembridge, Some combinatorial aspects of the spectra of normally distributed random matrices, Contemp. Math. 138 (1992), 7.
288. J. H. Hannay, Chaotic analytic zero points: exact statistics for those of a random spin state, J. Phys. A 29 (1996), L101-L105.
289. J.P. Hansen and I.R. McDonald, Theory of simple liquids, 2nd ed., Academic Press, London, 1990.
290. G.H. Hardy and J.E. Littlewood, Some problems of "Partitio Numerorum" III. On the expression of a number as a sum of primes, Acta Math. 44 (1923), 7.
291. J. Harer and D. Zagier, The Euler characteristic of the moduli space of curves, Inven. Math. 85 (1986), 457-485.
292. Harish-Chandra, Differential operators on a semisimple Lie algebra, Amer. J.Math. 79 (1957), 87-120.
293. J. Harnad and A.Yu. Orlov, Determiantal identity for multilevel systems and finite determinantal point processes, arXiv:0712.3892, 2007.
294. S.P. Hastings and J.B. McLeod, A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation, Arch. Rat.Mech. Anal. 73 (1980), 31-51.
295. S. Helgason, Differential geometry and symmetric spaces, Academic, New York, 1962.
296. E. Hellmann, Einführung in die quantenchemie, Deuticke, Vienna, 1937.
297. K. Hikami, Dunkl operator formalism for quantum many body problems associated with classical root systems, J. Phys. Soc. Japan 65 (1996), 7.
298. J.B. Hough, M. Krishnapur, Y. Peres, and B. Viŕag, Zeros of Gaussian analytic functions and determinantal point processes, American Mathematical Society, Providence, RI, 2009.
299. P.L. Hsu, On the distribution of the roots of certain determinantal equations, Ann. Eugen. 9 (1939), 250-258.
300. L.K. Hua, Analysis of functions of several complex variables in the classical domains, American Mathematical Society, Providence, RI, 1963.
301. A. Hurwitz, Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Nachr. Ges. Wiss. Göttingen (1898), 309-316.
302. A. Hurwitz, Mathematische werke, vol. 2, Birkhäuser, Basel, 1933.
303. M. Ishikawa, S. Okada, and M. Wakayama, Applications of minor summation formula. I Littlewood's formulas, J. Algebra 183 (1996), 193-216.
304. M. Ishikawa and M. Wakayama, Minor summation formulas of Pfaffians, Linear and Multilinear Algebra 39 (1995), 285-305.
305. M.E. Ismail, An electrostatics model for zeros of general orthogonal polynomials, Pacific J. Math. 193 (1999), 153-169.
306. M.E.H. Ismail and N.S. Witte, Discriminants and functional equations for polynomials orthogonal on the unit circle, J. Approx. Theory 110 (2001), 200-228.
307. A.R. Its, A.G. Izergin, V.E. Korepin, and N.A. Slavnov, Differential equations for quantum correlation functions, Int. J. Mod. Phys B 4 (1990), 1003-1037.
308. A.R. Its and A.V. Kitaev, Mathematical aspects of the non-perturbative 2d quantum gravity, Mod. Phys Lett. A5 (1990), 2079-2083.
309. C. Itzykson and J.B. Zuber, Planar approximation 2, J. Math. Phys. 21 (1980), 411-421.
310. K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida, From Gauss to Painlevé. a modern theory of special functions, Vieweg-Verlag, Braunschweig, 1991.
311. A.D. Jackson, M.K. Şener, and J.J.M. Verbaarschot, Finite volume partition functions and Itzyson-Zuber integrals, Phys. Lett. B 387 (1997), 355-360.
312. A.T. James, Distributions of matrix variate and latent roots derived from normal samples, Ann. Math. Statist. 35 (1964), 475-501.
313. B. Jancovici, Exact results for the two-dimensional one-component plasma, Phys. Rev. Lett. 46 (1981), 386-388.
314. B. Jancovici, Classical Coulomb systems near a plane wall. II, J. Stat. Phys. 29 (1982), 263-280.
315. B. Jancovici, Sum rules for the one-component plasma, unpublished note, 1994.
316. B. Jancovici, Classical Coulomb systems: screening and correlations revisited, J. Stat. Phys. 80 (1995), 445-459.
317. B. Jancovici, Pressure and Maxwell tensor in a Coulomb fluid, cond-mat/99112246, 1999.
318. B. Jancovici and P.J. Forrester, Derivation of an asymptotic expression in Beenakker's general fluctuation formula for correlations near an edge, Phys. Rev. B 50 (1994), 14599-14600.
319. B. Jancovici, J.L. Lebowitz, and G. Manificat, Large charge fluctuations in classical Coulomb systems, J. Stat. Phys. 72 (1993), 773-787.
320. B. Jancovici, G. Manificat, and C. Pisani, Coulomb systems seen as critical systems: finite-size effects in two dimensions, J. Stat. Phys. 76 (1994), 307-330.
321. B. Jancovici and G. Téllez, Two-dimensional Coulomb systems on a surface of constant negative curvature, J. Stat. Phys. 91 (1998), 953-977.
322. R.A. Janik and M.A. Nowak, Wishart and anti-Wishart random matrices, J. Phys. A 36 (2003), 3629-3637.
323. M. Jimbo and T. Miwa, Monodromony preserving deformations of linear ordinary differential equations with rational coefficients II, Physica 2D (1981), 407-448.
324. M. Jimbo, T. Miwa, Y. M̂ori, and M. Sato, Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent, Physica 1D (1980), 80-158.
325. M. Jimbo, T. Miwa, and K. Ueno, Monodromony preserving deformations of linear ordinary differential equations with rational coefficients I, Physica 2D (1981), 306-352.
326. S. Jitomirskaya, H. Schulz-Blades, and G. Stolz, Delocalization in random polymer models, Commun. Math. Phys. 233 (2003), 27-48.
327. K. Johansson, On Szegö's asymptotic formula for Toeplitz determinants and generalizations, Bull. Sci.Math., 2nd s ér 112 (1988), 257-304.
328. K. Johansson, On fluctuation of eigenvalues of random Hermitian matrices, Duke Math. J. 91 (1998), 151-204.
329. K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. 209 (2000), 437-476.
330. K. Johansson, Non-intersecting paths, random tilings and random matrices, Prob. Theory Related Fields 123 (2002), 225-280.
331. K. Johansson, Discrete polynuclear growth and determinantal processes, Commun. Math. Phys. 242 (2003), 277-329.
332. K. Johansson, personal communication, 2005.
333. K. Johansson and E. Nordenstam, Eigenvalues of GUE minors, Elect. J. Probability 11 (2006), 1342-1371.
334. I.M. Johnstone, On the distribution of the largest principal component, Ann. Math. Stat. 29 (2001), 295-327.
335. R.C. Jones, J.M. Kosterlitz, and D.J. Thouless, The eigenvalue spectrum of a large symmetric random matrix with a finite mean, J. Phys. A 11 (1978), L45-L48.
336. K.W.J. Kadell, A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris, SIAM J. Math. Anal. 19 (1988), 969-986.
337. K.W.J. Kadell, A proof of the q-Macdonald-Morris conjecture for BCn, Mem. Amer.Math. Soc. 108 (1994).
338. K.W.J. Kadell, The Selberg-Jack symmetric functions, Adv. Math. 130 (1997), 33-102.
339. K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta, and Y. Yamada, Determinant formulas for the Toda and discrete Toda equations, Funkcialaj Ekvacioj 44 (2001), 291-307.
340. P. Kalinay, P. Markos, L. Samaj, and I. Travenec, The sixth-moment sum rule for the pair correlations of the two-dimensional one-component plasma: exact results, J. Stat. Phys. 98 (2000), 639-666.
341. F. Kalisch and D. Braak, Exact density of states for finite Gaussian random matrix ensembles via supersymmetry, J. Phys. A 35 (2002), 9957-9969.
342. J. Kaneko, Selberg integrals and hypergeometric functions associated with Jack polynomials, SIAMJ.MathAnal. 24 (1993), 1086-1110.
343. J. Kaneko, Constant term identities of Forrester-Zeilberger-Cooper, Discrete Math. 173 (1997), 79-90.
344. E. Kanzieper, Eigenvalue correlations in non-Hermitian symplectic random matrices, J. Phys. A 35 (2002), 6631-6644.
345. E. Kanzieper and V. Freilikher, Two band random matrices, Phys. Rev. E 57 (1998), 6604-6611.
346. A.A. Kapaev and E. Hubert, A note on the Lax pairs for Painlevé equations, J. Math. Phys. 32 (1999), 8145-8156.
347. S. Karlin and L. McGregor, Coincidence probabilities, Pacific J. Math. 9 (1959), 1109-1140.
348. M. Katori and N. Komatsuda, Moments of vicious walkers and Möbius graph expansions, Phys. Rev. E 67 (2003), 051110.
349. M. Katori and H. Tanemura, Scaling limit of vicious walks and two-matrix model, Phys. Rev. E 66 (2002), 011105.
350. M. Katori and H. Tanemura, Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems, J. Math. Phys. 45 (2004), 7.
351. N.M. Katz and P. Sarnak, Random matrices, Frobenius eigenvalues, and monodromy, Colloquium publications, vol. 45, American Mathematical Society, Providence, RI, 1999.
352. N.M. Katz and P. Sarnak, Zeroes of zeta functions and symmetry, Bull. Amer. Math. Soc. 36 (1999), 1-26.
353. J.P. Keating, The Riemann zeta function and quantum chaology, Quantum Chaos (I. Guarneri and U. Smilansky, eds.), North Holland, Amsterdam, 1993, pp. 145-185.
354. J.P. Keating and N.C. Snaith, Random matrix theory and ζ(1/2 + it), Commun. Math. Phys. 214 (2001), 57-89.
355. R. Killip, Gaussian fluctuations for β ensembles, Int. Math. Res. Not. 2008 (2008), rnn007.
356. R. Killip and I. Nenciu, Matrix models for circular ensembles, Int. Math. Res. Not. 50 (2004), 2665-2701.
357. R. Killip and M. Stoiciu, Eigenvalue statistics for CMV matrices: from Poisson to clock via circular beta ensembles, Duke Math. J. 146 (2009), 361-399.
358. F. Knop, Symmetric and non-symmetric quantum Capelli polynomials, Comm. Math. Helv. 72 (1997), 84-100.
359. F. Knop and S. Sahi, A recursion and combinatorial formula for Jack polynomials, Inv. Math. 128 (1997), 9-22.
360. D.E. Knuth, Permutations, matrices and generalized Young tableaux, Pacific J. Math. 34 (1970), 709-727.
361. H. Kohler, Exact diagonalisation of 1-d interacting spinless fermions, arXiv:0801.0132, 2008.
362. I.K. Kostov, Conformal field theory techniques in random matrix ensembles, hep-th/9907060, 1999.
363. I. Krasovsky, Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on the unit circle, Int. Math. Res. Not. 2004 (2004), 1249-1272.
364. C. Krattenthaler, Generating functions for plane partitions of a given shape, Manuscripta Math. 69 (1990), 173-202.
365. C. Krattenthaler, A.J. Guttmann, and X.G. Viennot, Vicious walkers, friendly walkers and Young tableaux II: with a wall, J. Phys. A 33 (2000), 8835-8866.
366. M. Krishnapur, Zeros of random analytic functions, Ann. Prob. 37 (2009), 314-346.
367. H. Kunz, The one-dimensional classical electron gas, Ann. Phys. (N.Y.) 85 (1974), 303-335.
368. H. Kunz, The probability distribution of the spectral form factor in random matrix theory, J. Phys. A 32 (1999), 2171-2182.
369. V.B. Kuznetsov, V.V. Mangazeev, and E.K. Sklyanin, q-operator and factorized separation chain for Jack polynomials, Indag. Math. 14 (2003), 451-482.
370. L. Lapointe, A. Lascoux, and J. Morse, Determinantal formula and recursion for Jack polynomials, Electro. J. Comb. 7 (2001), 467.
371. N. Lehmann and H.-J. Sommers, Eigenvalue statistics of random real matrices, Phys. Rev. Lett. 67 (1991), 941-944.
372. A. Lenard, Correlation functions and the uniqueness of the state in classical statitical mechanics, Comm. Math. Phys. 30 (1973), 35-44.
373. I.G. Macdonald, Hypergeometric functions, unpublished manuscript.
374. I.G. Macdonald, Affine root systems and Dedekind's eta function, Inven. Math. 15 (1972), 91-143.
375. I.G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 998-1007.
376. I.G. Macdonald, Hall polynomials and symmetric functions, 2nd ed., Oxford University Press, Oxford, 1995.
377. C.C. MacDuffee, Vectors and matrices, Mathematical Association of America, Buffalo, NY, 1943.
378. A.M.S. Macêdo, Universal parametric correlations at the soft edge of the spectrum of random matrices, Europhys. Lett. 26 (1994), 641-646.
379. U. Magnea, Random matrices beyond the Cartan classification, J. Phys. A 71 (2008), 045203(27pp).
380. C. Mahaux and H.A.Weidenmüller, Shell-model approach to nuclear reactions, North Holland, New York, 1969.
381. G. Mahoux and M.L. Mehta, A method of integration over matrix variables IV, J. Physique I (France) 1 (1991), 1093-1108.
382. E. Majorana, Atomi orientati in campo magnetico variablile, Nuovo Cimento 9 (1932), 43-50.
383. J. Malmquist, Sur les équations différentialles du second ordre dont l'int égrale générale a ses points critiques fixes, Arkiv Mat. Astron. Fys. 18 (1922), 1-89.
384. F. Marcellan and R. Alvarez-Nordarse, On the "Favard theorem" and its extensions, J. Comput. Appl. Math. 127 (2001), 231-254.
385. M. Marino, Chen-Simon thoery, matrix integrals and perturbative three-manifold invariants, Commun. Math. Phys. 253 (2005), 25-49.
386. Ph. A. Martin, Sum rules in charged fluids, Rev. Mod. Phys. 60 (1988), 1075-1127.
387. Ph. A. Martin and Ch. Gruber, A new proof of the Stillinger-Lovett complete shielding condition, J. Stat. Phys. 31 (1983), 691-710.
388. V.A. Marčenko and L.A. Pastur, Distributions of eigenvalues for some sets of random matrices, Math. USSRSbornik 1 (1967), 457-483.
389. A.M. Mathai, Jacobians of matrix transformations and functions of matrix arguments, World Scientific, Singapore, 1997.
390. D.C. Mattis, Statistical mechanics made simple, 2nd ed., World Scientific, River Edge, NJ, 2008.
391. R.E McMurtrie, Determinants of stability of large randomly connected systems, J. Theor. Biol. 50 (1975), 1-11.
392. M.L. Mehta, Random matrices and the statistical theory of energy levels, Academic Press, New York, 1967.
393. M.L. Mehta, Matrix theory, éditions de Physique, Les Ulis, France, 1989.
394. M.L. Mehta, A non-linear differential equation and a Fredholm determinant, J. de Physique I (France) 2 (1991), 1721-1729.
395. M.L. Mehta, Random matrices, 2nd ed., Academic Press, New York, 1991.
396. M.L. Mehta, Power series for level spacing functions of random matrix ensembles, Z. Phys. B 86 (1992), 285-290.
397. M.L. Mehta and F.J. Dyson, Statistical theory of the energy levels of complex systems. V, J. Math. Phys. 4 (1963), 713-719.
398. P.A. Mello, Averages on the unitary group and applications to the problem of disordered conductors, J. Phys. A 23 (1990), 4061-4080.
399. P.A. Mello, A. Pereyra, and N. Kumar, Macroscopic approach to multichannel disordered conductors, Ann. Phys. 181 (1988), 290-317.
400. P.A. Mello, P. Pereyra, and T.H. Seligman, Information theory and statistical nuclear reactions I, Ann. Phys. (N.Y.) 161 (1985), 254-275.
401. A. Messiah, Quantum mechanics, vol. I and II, North Holland, Amsterdam, 1972.
402. F. Mezzadri, How to generate random matrices from the classical groups, Notices AMS 54 (2007), 592-604.
403. S.J. Miller and R. Takloo-Bighash, An invitation to modern number theory, Princeton University Press, Princeton, NJ, 2006.
404. K. Mimachi, A duality of Macdonald-Koornwinder polynomials and its application to integral representations, Duke Math. J 107 (2001), 265-281.
405. H.L. Montgomery, The pair correlation of zeros of the zeta function, Proc. Sympos. PureMath., vol. 24, American Mathematical Society, Providence, RI, 1973, pp. 181-193.
406. E.H. Moore, On the determinant of a Hermitian matrix of quaternionic elements, Bull.Am. Math. Soc. 28 (1922), 161-162.
407. W. G. Morris, Constant term identities for finite and affine root systems, conjectures and theorems, Ph.D. thesis, University of Wisconsin, 1982.
408. P.M. Morse and H. Feshbach, Methods of theoretical physics, vol. 2, McGraw-Hill, New York, 1953.
409. M. Moshe, H. Neuberger, and B. Shapiro, Generalized ensemble of random matrices, Phys. Rev. Lett. 73 (1994), 1497-1500.
410. R.J. Muirhead, Aspects of multivariate statistical theory, Wiley, New York, 1982.
411. F.D. Murnaghan, The unitary and rotation groups, Spartan Books, Washington DC, 1962.
412. N.I. Muskhelishvili, Singular integral equations, 2nd ed., Dover, New York, 1992.
413. K.A. Muttalib, Y. Chen, M.E.H. Ismail, and V.N. Nicopolous, New family of unitary random matrices, Phys. Rev. Lett. 71 (1994), 471-474.
414. T. Nagao, Universal correlations near a singularity of random matrix spectrum, J. Phys. Soc. Japan 64 (1995), 3675-3681.
415. T. Nagao and P.J. Forrester, Asymptotic correlations at the spectrum edge of random matrices, Nucl. Phys. B 435 (1995), 401-420.
416. T. Nagao and P.J. Forrester, Multilevel dynamical correlation functions for Dyson's Brownian motion model of random matrices, Phys. Lett. A 247 (1998), 42-46.
417. T. Nagao and P.J. Forrester, Quaternion determinant expressions for multilevel dynamical correlation functions of parametric random matrices, Nucl. Phys. B 563 (1999), 547-572.
418. T. Nagao and K. Slevin, Laguerre ensembles of random matrices: nonuniversal correlation functions, J. Math. Phys. 34 (1993), 2317-2330.
419. T. Nagao and M. Wadati, Correlation functions of random matrix ensembles related to classical orthogonal polynomials, J. Phys. Soc. Japan 60 (1991), 3298-3322.
420. T. Nagao and M. Wadati, Correlation functions of random matrix ensembles related to classical orthogonal polynomials II, III, J. Phys. Soc. Japan 61 (1992), 78-88, 1910-1918.
421. T. Nagao and M. Wadati, Correlation functions for Jastrow-product wave functions, J. Phys. Soc. Japan 62 (1993), 480-488.
422. F. Nijhoff, J. Satsuma, K. Kajiwara, B. Grammaticos, and A. Ramani, A study of the alternate discrete Painlevé II equation, Inverse problems 12 (1996), 697-716.
423. E.J.G. Nordenstam, Erratum to eigenvalues of GUE minors, Elect. J. Probability 12 (2007), 1048-1051.
424. M. Noumi and Y. Yamada, Higher order Painlevé equations of type A(1) l, Funkcial. Ekvac 41 (1998), 483-503.
425. A.M. Odlyzko, On the distribution of spacings between zeros of the zeta function, Math. Comput. 48 (1987), 273-308.
426. A.M. Odlyzko, The 1020th zero of the Riemann zeta function and 70 million of its neighbours, Preprint, 1989.
427. K. Okamoto, Polynomial Hamiltonians associated with Painlevé equations, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 264-268.
428. K. Okamoto, Studies of the Painlevé equations I. Sixth Painlevé equation PV I, Ann. Math. Pura Appl. 146 (1987), 337-381.
429. K. Okamoto, Studies of the Painlevé equations IV. Third Painlevé equation PIII, Funkcialaj. Ekvacioj. 30 (1987), 305-332.
430. A. Okounkov, Infinite wedge and random partitions, Selecta Math. (N.S.) 7 (2001), 57-81.
431. A. Okounkov and G. Olshanski, Shifted Jack polynomials, binomial formula and applications, Math. Res. Lett. 4 (1997), 69-78.
432. A. Okounkov and G. Olshanski, Shifted Schur polynomials, binomial formula and applications, Math. Res. Lett. 4 (1997), 533-553.
433. I. Olkin, The 70th anniversary of the distribution of random matrices: a survey, Linear Algebra Appl. 354 (2002), 231-243.
434. M.A. Olshanetsky and A.M. Perelomov, Quantum integrable systems related to Lie algebras, Phys. Rep. 94 (1983), 313-404.
435. F. Olver, Asymptotics and special functions, Academic Press, London, 1974.
436. E.M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75-121.
437. E.M. Opdam, Lectures on Dunkl operators, Math. Soc. Japan Mem. 8 (1998), 1-62.
438. A.Y. Orlov, New solvable matrix integrals, Int. J. Mod. Phys. A 19 (2004), 276-293.
439. J.C. Osborn, Universal results from an alternative random matrix model for QCD with a baryon chemical potential, Phys. Rev. Lett. 93 (2004), 222001.
440. A. Pandey, Statistical properties of many-particle spectra III., Ann. Phys. 119 (1979), 170-191.
441. A. Pandey and M.L. Mehta, Gaussian ensembles of random Hermitian matrices intermediate between orthogonal and unitary ones, Commun. Math. Phys. 87 (1983), 449-468.
442. S. Péché, The largest eigenvalue of small rank perturbations of Hermitian random matrices, Prob. Theory Related Fields 134 (2006), 127-173.
443. Y. Peres and B. Virág, Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process, Acta. Math. 194 (2005), 1-35.
444. N. Du Plessis, An introduction to potential theory, Oliver and Boyd, Edinburgh, 1970.
445. H.D. Politzer, Random-matrix description of the distribution of mesoscopic conductance, Phys. Rev. B 40 (1989), 11917-11919.
446. A.P. Polychronakos, Exhange operator formalism for integrable systems of particles, Phys. Rev. Lett. 69 (1992), 703.
447. C.E. Porter, Statistical theories of spectra: fluctuations, Academic Press, New York, 1965.
448. D. Porter and D.S.G. Stirling, Integral equations: a practical treatment, from spectral theory to applications, Cambridge University Press, Cambridge, 1990.
449. M. Prähofer, High precision moments corresponding to GUE/GOE/GSE, Unpublished note, 2004.
450. M. Prähofer and H. Spohn, Universal distributions for growth processes in 1+1 dimensions and random matrices, Phys. Rev. Lett. 84 (2000), 4882-4885.
451. M. Prähofer and H. Spohn, Exact scaling functions for one-dimensional stationary KPZ growth, J. Stat. Phys. 108 (2004), 1071-1106.
452. R.A. Proctor, Odd symplectic groups, Inv.Math. 92 (1988), 307-332.
453. R.A. Proctor, Equivalence of the combinatorial and the classical definitions of Schur functions, J. Combin. Theory A 51 (1989), 135-137.
454. E.M. Rains, Attack of the zonal polynomials, Preprint, 1995.
455. E.M. Rains, Increasing subsequences and the classical groups, Elect. J. of Combinatorics 5 (1998), #R12.
456. E.M. Rains, Correlations for symmetrized increasing subsequences, math.CO/0006097, 2000.
457. E.M. Rains, Unpublished notes, 2001,04.
458. E.M. Rains, Images of eigenvalue distributions under power maps, Prob. Theory Related Fields 125 (2003), 522-538.
459. E.M. Rains, Limits of elliptic hypergeometric integrals, Ramanujan J. 18 (2009), 257-306.
460. E.M. Rains and M. Vazirani, Vanishing integrals of Macdonald and Koornwinder polynomials, Transform. Groups 12 (2007), 725-759.
461. A. Ramani, Y. Ohta, and B. Grammaticos, Discrete integrable systems from continuous Painlevé equations through limiting procedures, Nonlinearity 13 (2000), 1073-1085.
462. J. Ramirez and B. Rider, Diffusion at the random matrix hard edge, arXiv:0803.2043, 2008.
463. J. Ramirez, B. Rider, and B. Virag, Beta ensembles, stochastic Airy spectrum, and a diffusion, arXiv:math/060733, 2006.
464. A. Raposo, H.J. Weber, D.E. Alvarez, and M. Kirchback, Romanovski polynomials in selected physics problems, Central Europ. J. Phys. 5 (2007), 253-284.
465. B. Rider, Deviations from the circular law, Prob. Theory Related Fields 130 (2003), 337-367.
466. B. Rider, A limit theorem at the edge of a non-Hermitian random matrix ensemble, J. Phys. A 36 (2003), 3401-3410.
467. B. Rider, Order statistics and Ginibre's ensemble, J. Stat. Phys. 114 (2004), 1139-1148.
468. B. Rider and B. Virág, The noise in the circular law and the Gaussian free field, Int. Math. Res. Not. 2007 (2007), rnm006(32 pp).
469. H. Risken, The Fokker-Planck equation, Springer, Berlin, 1992.
470. V. Romanovsky, Sur quelques classes nouvelles de polynômes orthogonaux, C.R. Acad. Sci. Paris 188 (1929), 1023-1025.
471. M. Rubinstein, Computational methods and experiments in analytic number theory, Recent perspectives in random matrix theory and number theory (F. Mezzadri and N.C. Snaith, eds.), London Mathematical Society Lecture Note Series, vol. 322, Cambridge University Press, Cambridge, 2005, pp. 425-506.
472. Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math. J. (1995), 269-322.
473. E. Ryckman, Linear statistics of point processes via orthogonal polynomials, J. Stat. Phys. (2008), 473-486.
474. E. Saff and A. Kuijlaars, Distributing many points on a sphere, Math. Intelligencer 10 (1997), 5-11.
475. B.E. Sagan, The symmetric group, 2nd ed., Springer, New York, 2000.
476. S. Sahi, A new scalar product for nonsymmetric jack polynomials, Int. Math. Res. Not. (20) (1996), 997-1004.
477. S. Sahi, The binomial formula for nonsymmetric Macdonald polynomials, Duke Math. J. 1998 (1998), 465-477.
478. H. Sakai, Rational surfaces associated with affine root systems and geometry of the Painlevé equations, Commun. Math. Phys. 220 (2001), 165-229.
479. L. Samaj and J.K. Percus, A functional relation among the pair correlations of the two-dimensional onecomponent plasma, J. Stat. Phys. 80 (1995), 495-512.
480. T. Sasamoto, Spatial correlations of the 1D KPZ surface on a flat substrate, J. Phys. A 38 (2005), L549-L556.
481. C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1963), 179-191.
482. B. Schlittgen and T. Wettig, Generalizations of some integrals over the unitary group, J. Phys. A 36 (2003), 3195-3202.
483. A. Selberg, Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr. 24 (1944), 71-78.
484. D. Serban, Some properties of the Calogero-Sutherland model with reflections, J. Phys. A 30 (1997), 4215-4225.
485. T. Shifrin, Multivariable mathematics, Wiley, New York, 2005.
486. J.W. Silverstein, The smallest eigenvalues of a large dimensional Wishart matrix, Ann. Probab. 13 (1985), 1364-1368.
487. S.H. Simon and A. L. Moustakas, Crosssover from conserving to lossy transport in circular random-matrix ensembles, Phys. Rev. Lett. 96 (2006), 136805.
488. S.H. Simon, A. L. Moustakas, and L. Marinelli, Capacity and character expansions: moment generating function and other exact results for MIMO correlated channels, IEEE Trans. Inform. Theory 52 (2006), 5336-5351.
489. S.H. Simon, A. L. Moustakas, M. Stoytchev, and H. Safar, Communication in a disordered world, Physics Today 54 (2001), 38.
490. B.D. Simons and B. L. Altshuler, Universal velocity correlations in disordered and chaotic systems, Phys. Rev. Lett. 70 (1993), 4063.
491. C.D. Sinclair, Averages over Ginibre's ensemble of random real matrices, Int. Math. Res. Not. 2007 (2007), rnm015.
492. K. Slevin and T. Nagao, Impurity scattering in mesoscopic quantum wires and the Laguerre ensemble, Phys. Rev. B 50 (1994), 2380-2392.
493. E.R. Smith, Effects of surface charge on the two-dimensional one-component plasma: I. Single double layer, J. Phys. A 15 (1982), 3861-3868.
494. A. Soshnikov, Level spacings distribution for large random matrices: Gaussian fluctuations, Ann. Math. 148 (1998), 573-617.
495. A. Soshnikov, Determinantal random point fields, Russian Math. Surveys 55 (2000), 923-975.
496. A. Soshnikov, A note on the universality of the distribution of the largest eigenvalues in certain sample covariance matrices, J. Stat. Phys. 108 (2002), 1033-1056.
497. A. Soshnikov, Statistics of extreme spacing in determinantal random point processes, Mosc. Math. J. 5 (2007), 705-719.
498. A. Soshnikov, Gaussian fluctuation for the number of particles in Airy, Bessel, Sine, and other determinantal random point fields, J. Stat. Phys. 100 (2000), 491-522.
499. A. Sri Ranga and W. Van Assche, Blumenthal's theorem for Laurent orthogonal polynomials, J. Approx. Th. 117 (2002), 255-278.
500. R.P. Stanley, Some combinatorial properties of Jack symmetric functions, Advan. Math. 77 (1989), 76-115.
501. R.P. Stanley, Enumerative combinatorics, vol. 2, Cambridge University Press, Cambridge, 1999.
502. J.R. Stembridge, Non-intersecting paths, Pfaffians and plane partitions, Adv. Math. 83 (1990), 96-131.
503. T.J. Stieltjes, Sur quelques theórems d'algébra, Oeuvres complétes, vol. 1, Société Mathématique d'Amsterdam, Groningen, 1914, pp. 440-441.
504. A.D. Stone, P.A. Mello, K.A. Muttalib, and J.-L. Pichard, Random matrix theory and maximum entropy models for disordered conductors, Mesoscopic phenomena in solids (P.A. Lee B.L. Altshuler and R.A.Webb, eds.), North Holland, Amsterdam, 1991, pp. 369-448.
505. B. Sutherland, Exact results for a quantum many body problem in one dimension, Phys. Rev. A 4 (1971), 2019-2021.
506. B. Sutherland, Quantum many-body problem in one dimension, J. Math. Phys. 12 (1971), 246-250.
507. B. Sutherland, Exact ground state wave function for a one-dimensional plasma, Phys. Rev. Lett. 34 (1975), 1083-1085.
508. G. Szegö, Orthogonal polynomials, 4th ed., American Mathematical Society, Providence RI, 1975.
509. A. Takemura, Zonal polynomials, Institute of Mathematical Statistics, Hayward, CA, 1984.
510. T. Tao and V. Vu, Random matrices: universality of esds and the circular law, arXiv:0807.4898, 2008.
511. G. Telléz and P.J. Forrester, Finite size study of the 2dOCP atΓ = 4 and Γ = 6, J. Stat. Phys. 97 (1999), 489-521.
512. N.M. Temme, Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function, Math. Comp. 29 (1975), 1109.
513. Y. Tian, Matrix representations of octonions and their applications, Adv. Appl. Clifford Algebras 10 (2000), 61-90.
514. M. Tierz, Soft matrix models and chern-simons partition functions, Mod. Phys. Lett. A 19 (2004), 1365-1378.
515. E.C. Titchmarsh, Theory of functions, Oxford University Press, London, 1939.
516. E.C. Titchmarsh, The theory of the Riemann zeta function, 2nd ed., Clarendon Press, Oxford, 1986.
517. C.A. Tracy and H.Widom, Introduction to random matrices, Geometric and quantum aspects of integrable systems (G.F. Helminck, ed.), Lecture Notes in Physics, vol. 424, Springer, New York, 1993, pp. 407-424.
518. C.A. Tracy and H.Widom, Fredholm determinants, differential equations and matrix models, Commun. Math. Phys. 163 (1994), 33-72.
519. C.A. Tracy and H.Widom, Level-spacing distributions and the Airy kernel, Commun. Math. Phys. 159 (1994), 151-174.
520. C.A. Tracy and H.Widom, Level-spacing distributions and the Bessel kernel, Commun. Math. Phys. 161 (1994), 289-309.
521. C.A. Tracy and H.Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996), 727-754.
522. C.A. Tracy and H.Widom, Correlation functions, cluster functions and spacing distributions in random matrices, J. Stat. Phys. 92 (1998), 809-835.
523. A.M. Tulino and S. Verdú, Random matrix theory and wireless communications, Foundations and Trends in Communcations and Information Theory, vol. 1, Now Publisher, 2004, pp. 1-182.
524. B. Valkó and B. Virág, Continuum limits of random matrices and the Brownian carousel, Inv. Math. 177 (2008), 463-508.
525. B. Valkó and B. Virág, Large gaps between random eigenvalues, arXiv:0811.0007, 2008.
526. P. van Moerbeke, Integrable lattices: random matrices and random permutations, Random matrix models and their applications (P.M. Bleher and A.R. Its, eds.), Mathematical Sciences Research Institute Publications, vol. 40, Cambridge University Press, Cambridge, 2001, pp. 321-406.
527. R. Vein and P. Dale, Determinants and their applications in mathematical physics, Springer, New York, 1999.
528. A.M. Veneziani, T. Pereira, and D.H.U. Marchetti, Conformal universality in normal matrix ensembles, arXiv:0909.3418, 2009.
529. J.J.M. Verbaarschot, The spectrum of the Dirac operator near zero virtuality for nc = 2and chiral random matrix theory, Nucl. Phys. B 426 (1994), 559-574.
530. J.J.M. Verbaarschot and T.Wettig, Random matrix theory and chiral symmetry in QCD, Ann. Rev. Nucl. Part. Sci. 50 (2000), 343-410.
531. J.M. Verbaarschot, H.A.Weidenmüller, and M.R. Zirnbauer, Grassman integration in stochastic quantum physics: the case of compound nucleus scattering, Phys. Rep. 129 (1985), 367-438. \
532. G. Viennot, Une forme geóm étrique de la correspondance de Robinson-Schensted, Combinatoire et repr ésentation du groupe symétrique (D. Foata, ed.), Lecture Notes in Mathematics, vol. 579, Springer, Berlin, 1977, pp. 29-58.
533. J.P. Vinson, Closest spacing of eigenvalues, Ph.D. thesis, Princeton University, 2001.
534. F. von Oppen, Exact distribution of eigenvalue curvatures of chaotic quantum systems, Phys. Rev. Lett. 73 (1994), 798-801.
535. K.W. Wachter, The strong limits of random matrix spectra for sample matrices of independent elements, Annal. Prob. 6 (1978), 1-18.
536. K.W. Wachter, The limiting measure of multiple disriminant ratios, Ann. Statist. 8 (1980), 937-957.
537. S.O. Warnaar, On the generalized Selberg integral of Richards and Zheng, Adv. Applied Math. 40 (2008), 212-218.
538. H. Watanabe, Defining variety and birational canonical transformations of the fifth Painlevé equation, Analysis 18 (1998), 351-357.
539. G.N. Watson, Theory of Bessel functions, 2nd ed., Cambridge University Press, Cambridge, 1966.
540. H. Weyl, The classical groups: Their invariants and representations, Princeton University Press, Princeton, NJ, 1939.
541. E.T. Whittaker and G.N. Watson, A course of modern analysis, 2nd ed., Cambridge University Press, Cambridge, 1965.
542. H. Widom, Strong Szegö theorem on circular arcs, Indiana Univ. Math. J. 21 (1971), 277-283.
543. H. Widom, The asymptotics of a continuous analogue of orthogonal polynomials, J. Approx. Theory 77 (1996), 51-64.
544. H. Widom, On the relation between orthogonal, symplectic and unitary random matrices, J. Stat. Phys. 94 (1999), 347-364.
545. H.S. Wilf, Ascending subsequences of permutations and the shapes of tableaux, J. Combin. Theory Ser. A 60 (1992), 155-157.
546. J.H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965.
547. J. Wishart, The generalized product moment distribution in samples from a normal multivariate population, Biometrika 20A (1928), 32-43.
548. N.S.Witte, Gap probabilities for double intervals in Hermitian random matrix ensembles as τ-functions-spectrum singularity case, Lett.Math. Phys. 68 (2004), 139-149.
549. T.T. Wu and C.N. Yang, Dirac monopole without string: monopole harmonics, Nucl. Phys. B 107 (1976), 365-380.
550. Z. Yan, A class of generalized hypergeometric functions in several variables, Canad. J. Math. 44 (1992), 1317-1338.
551. I. Zakharevich, A generalization of Wigner's law, Comm. Math. Phys. 268 (2006), 403-414.
552. D. Zeilberger, A Stembridge-Stanton style elementary proof of the Habsieger-Kadell q Morris identity, Discrete Math. 79 (1989), 313-322.
553. A. Zhedanov, Biorthogonal rational functions and the generalized eigenvalue problem, J. Approx. Th. 101 (1999), 303-329.
554. P. Zinn-Justin, Universality of correlation functions of Hermitian random matrices in an external field, Commun. Math. Phys. 194 (1998), 631-650.
555. P. Zinn-Justin, Some matrix integrals related to knots and links, Random matrix models and their applications (P.M. Bleher and A.R. Its, eds.), Mathematical Sciences Research Institute Publications, vol. 40, Cambridge University Press, Cambridge, 2001, pp. 421-438.
556. M.R. Zirnbauer, Riemannian symmetric superspaces and their origin, J. Math. Phys. 37 (1996), 4986-5018.
557. A. Zvonkin, Matrix integrals and map enumeration: an accessible introduction, Math. Comp. Modelling 26 (1997), 281-304.
558. K. Zyczkowski and M. Kus, Unitary random matrices, J. Phys. A 27 (1994), 4235-4245.
559. K. Zyczkowski and H.-J. Sommers, Truncations of random unitary matrices, J. Phys. A 33 (2000), 2045-2057.
560. K. Zyczkowski and H.-J. Sommers, Induced measures in the space of mixed quantum states, J. Phys. A 34 (2001), 7111-7125.