Developments in random matrix theory

Journal of Physics A: Mathematical and General

Volumn 36, Issue 12 SPEC. ISS., 2003, Pages

  Forrester, P J ^a   Snaith, N C ^b   Verbaarschot, J J M ^c  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041582120     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/12/201     Document Type: Review

References (129)

1. Guhr T, Mueller-Groeling A and Weidenmueller H A 1998 Random-matrix theories in quantum physics: common concepts Phys. Rep. 299 189
2. Wishart J 1928 Generalized product moment distribution in samples Biometrika A 20 32
3. Wigner E P 1951 On the statistical distribution of the widths and spacings of nuclear resonance levels Proc. Camb. Phil. Soc. 47 790
4. Wigner E P 1955 Characteristic vectors of bordered matrices with infinite dimensions Ann. Math. 62 548
5. Wigner E P 1957 Statistical properties of real symmetric matrices with many dimensions Can. Math. Congr. Proc. (Toronto: University of Toronto Press) p 174
6. Landau L and Smorodinsky Ya 1955 Lectures on the Theory of the Atomic Nucleus (Moscow: State Technical-Theoretical Literature Press) p 92
7. Gurevich I I and Pevsner M I 1957 Repulsion of nuclear levels Nucl. Phys. 2 575
8. Porter C E and Rosenzweig N 1960 Statistical properties of atomic and nuclear spectra Suomalaisen Tiedeakatemian Toimituksia AVI 44
9. Gaudin M 1961 Sur la loi limite de l'espacement des valeurs propres d'une matrice aléatoire Nucl. Phys. 25 447
10. Mehta M L 1960 On the statistical properties of level spacings in nuclear spectra Nucl. Phys. 18 395
11. Mehta M L 1960 L'emploi del polynomes orthogonaux pour calculer certain determinants Rapport S PH (Saclay) 658
12. Dyson F J 1962 Statistical theory of the energy levels of complex systems, I J. Math. Phys. 3 140
13. Dyson F J 1962 Statistical theory of the energy levels of complex systems, II J. Math. Phys. 3 157
14. Dyson F J 1962 Statistical theory of the energy levels of complex systems, III J. Math. Phys. 3 166
15. Dyson F J 1962 A Brownian motion model for the eigenvalues of a random matrix J. Math. Phys. 3 1191
16. Dyson F J 1962 The threefold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics J. Math. Phys. 3 1200
17. Balian R 1968 Random matrices and information theory Nuovo Cimenta B 57 183
18. Sutherland B 1971 Exact results for a quantum many-body system in one dimension Phys. Rev. A 4 2019
19. Calogero F 1971 Solution of one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials J. Math. Phys. 12 419
20. Forrester P J Log-gases and random matrices webpage http://www.ms.unimelb.edu.au/̃matjpf/matpjf.html
21. Korepin V E, Bogoliubov N M and Izergin A G 1993 Quantum Inverse scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
22. Mehta M L 1967 Random Matrices and the Statistical Theory of Energy Levels (New York: Academic)
23. Porter C E 1965 Statistical Theory of Spectra: Fluctuations (New York: Academic)
24. Anderson P W 1958 Absence of diffusion in certain random lattices Phys. Rev. 109 1492
25. Gorkov L P and Eliasberg G M 1965 Minute metallic particles in an electromagnetic field Sov. Phys.-JETP 21-940
26. Hua L K 1958 Harmonic Analysis of Functions of Many Complex Variables in Classical Domains (Peking: Science Press)
27. Harish-Chandra 1957 Differential operators on a semi-simple Lie algebra Am, J. Math. 79 85
28. Itzykson C and Zuber J-B 1980 Planar approximation 2 J. Math. Phys. 21 411
29. Zinn-Justin P and Zuber J-B 2003 On some integrals over the U(N) unitary group and their large N limit J. Phys. A: Math. Gen. 36 3173-93 (Preprint math-ph/0209019)
30. Selberg A 1944 Bemerkninger om et multipelt integral Nord. Mat. Tid. 26 71
31. Mehta M L 1991 Random Matrices 2nd edn (New York: Academic)
32. James A T 1961 Zonal polynomials of real positive definite symmetric matrices Ann. Math, 74 456
33. Muirhead R J 1982 Aspects of Multivariate Statistical Theory (New York: Wiley)
34. Girko V L 1990 Theory of Random Determinants (Dordrecht: Kluwer)
35. Voiculescu D 1991 Limit laws for random matrices and free products Invent. Math. 104 201
36. Efetov K B 1983 Supersymmetry and the theory of disordered metals Adv. Phys. 32 53
37. Efetov K B 1982 Level spacing distribution in small metallic particles J. Phys. G: Nucl, Phys. 15 L909
38. Efetov K B 1982 Supersymmetric method in the localization theory Zh. Eksp. Tear. Fiz. 82 872
39. Wigner E P 1951 On a class of analytic functions from the quantum theory of collisions Ann. Math. 53 36
40. Porter C E and Thomas R G 1956 Fluctuations of nuclear reaction widths Phys. Rev. 104 483
41. Ericson T 1960 Fluctuations of nuclear cross-sections in the continuum region Phys. Rev. Lett. 5 430
42. Agassi D, Mantzouranis G and Weidenmueller H A 1975 The statistical theory of nuclear reactions for strongly overlapping resonances as a theory of transport phenomena Phys. Rep. C 22 145
43. Abrikosov A A, Gorkov L P and Dzyaloshinski I E 1963 Methods of Quantum Field Theory in Statistical Physics (Engelwood Cliffs, NJ: Prentice-Hall)
44. Ginibre J 1965 Statistical ensembles of complex, quaternion and real matrices J Math. Phys. 6 440
45. Fyodorov Y V and Sommers H-J 2003 Random Matrices close to Hermitian or unitary: overview of methods and results J. Phys. A: Math. Gen. 36 3303-47 (Preprint nlin.CD/0207051)
46. Montgomery H L 1973 The pair correlation of the zeta function Proc. Symp. Pure Math. 24 181
47. Hejhal D A 1994 On the triple correlation of zeros of the zeta function Int. Math. Res. Not. 7 293
48. Rudnick Z and Sarnak P 1996 Zeros of principle L-functions and random matrix theory Duke Math. J. 81 269
49. Bogomolny E B and Keating J P 1995 Random matrix theory and the Riemann zeros I: three- and four-point correlations Nonlinearity 8 1115
50. Bogomolny E B and Keating J P 1996 Random matrix theory and the Riemann zeros II: n-point correlations Nonlinearity 9 911
51. Katz N M and Samak P 1999 Random Matrices, Frobenius Eigenvalues and Monodromy (Providence, RI: American Mathematical Society)
52. Conrey J B, Farmer D W, Keating J P, Rubinstein M O and Snaith N C 2002 Integral moments of zeta- and L-functions Preprint math.nt/0206018
53. Conrey J B, Farmer D W, Keating J P, Rubinstein M O and Snaith N C 2002 Autocorrelation of random matrix polynomials Preprint math-ph/0208007 (Commun. Math. Phys. at press)
54. Keating J P, Linden N and Rudnik Z 2003 Random matrix theory, the exceptional Lie groups and L-functions J. Phys. A: Math. Gen. 36 2933-4 (Preprint math-ph/0210058)
55. Keating J P and Snaith N C 2000 Random matrix theory and ζ(1/2 + it) Commun. Math. Phys. 214 57
56. Keating J P and Snaith N C 2000 Random matrix theory and L-functions at s = 1/2 Commun. Math. Phys. 214 91
57. Conrey J B, Keating J P, Rubinstein M O and Snaith N C 2001 On the frequency of vanishing of quadratic twists of modular L-fanctions Number Theory for the Millennium: Proc. of the Millennial Conf. on Number Theory ed B C Berndt (Boston: A K Peters) (Preprint math.nt/0012043)
58. Hughes C P 2003 Random matrix theory and discrete moments of the Riemann zeta function J. Phys. A: Math. Gen. 36 2907-17 (Preprint math.nt/0207236)
59. Hughes C P, Keating J P and O'Connell N 2000 Random matrix theory and the derivative of the Riemann zeta function Proc. R. Soc. A 456 2611
60. Mezzadri F 2003 Random matrix theory and the zeros of ζ ′(s) J. Phys. A: Math. Gen. 36 2945-62 (Preprint math-ph/0207044)
61. Keating J P and Snaith N 2003 Random matrices and L-functions J. Phys. A: Math. Gen. 36 2859-81
62. Edwards S F and Anderson P W 1975 Theory of spin glasses J. Phys. F: Met. Phys. 5 965
63. Wegner F J 1979 Mobility edge problem - continuous symmetry and a conjecture Z. Phys. B 35 209
64. Efetov K B, Larkin AI and Khemlnitsky D E 1980 Interaction of diffusion modes in the theory of localization Zh. Eksp. Teor. Fiz. 79 1120
65. McKane A J and Stone M 1981 Localization as an alternative to Goldstone theorem Ann. Phys., NY 131 36
66. Schaefer L and Wegner F J 1980 Disordered system with N-orbitals per site-Lagrange formulation, hyperbolic symmetry, and Goldstone modes Z. Phys. B 38 113
67. Thouless D J 1977 Maximum metallic resistance in thin wires Phys. Rev. Lett. 39 1167
68. Verbaarschot J J M, Weidenmueller H A and Zirnbauer M R 1985 Grassmann integration in stochastic quantum physics: the case of compound-nucleus scattering Phys. Rep. 129 367
69. Wegner F J 1983 Algebraic derivation of symmetry-relations for disordered electronic systems Z. Phys. B 49 297
70. Simons B D and Altshuler B L 1993 Universal velocity correlations in disordered and chaotic systems Phys. Rev. Lett. 70 4063
71. Efetov K B 1997 Supersymmetry in Disorder and Chaos (Cambridge: Cambridge University Press)
72. Mello P A, Pereyra P and Seligman T 1985 Information-theory and statistical nuclear reactions 1. General theory and applications to few-channel problems Ann. Phys., NY 161 254
73. Brody T A, Flores J, French J B, Mello P A, Pandey A and Wong S S M 1981 Random-matrix physics -spectrum and strength fluctuations Rev. Mod. Phys. 53 385
74. Benet L and Weidenmüller H A 2003 Review of the k-Body embedded ensembles of Gaussian random matrices J. Phys. A: Math. Gen. 36 3569-93 (Preprint cond-mat/0207656)
75. Webb R A, Washburn S, Umbach C P and Laibwitz R B 1985 Observation of H/ E Ahoronov-Bohm oscillations in normal-metal rings Phys. Rev. Lett. 54 2696
76. Altshuler B L 1985 Fluctuations in the extrinsic conductivity of disordered conductors Pis'ma Zh. Eksp. Teor. Fiz. 41 530
77. Stone A D 1985 Magnetoresistance fluctuations in mesoscopic wires and rings Phys. Rev. Lett. 54 2692
78. Lee P A and Stone A D 1985 Universal conductance fluctuations in metals Phys. Rev. Lett. 55 1622
79. Beenakker C W J 1997 Random-matrix theory of quantum transport Rev. Mod. Phys. 69 731
80. Alhassid Y 2000 The statistical theory of quantum dots Rev. Mod. Phys. 72 895
81. Polianski M L and Brouwer P W 2003 Scattering matrix ensemble for time-dependent transport through a chaotic quantum dot J. Phys. A: Math. Gen. 36 3215-36 (Preprint cond-mat/0208408)
82. 't Hooft G 1974 A two-dimensional model for mesons Nucl. Phys. B 75 461
83. Brezin E, Itzykson C, Parisi G and Zuber J B 1978 Planar diagrams Commun. Math. Phys. 59 35
84. Deift P P, Kriecherbauer T, McLaughlin K T R, Venakides S and Zhou X 1999 Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory Commun, Pure Appl. Math. 52 1335
85. Seiberg N and Witten E 1994 Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory Nucl. Phys. B 426 19 Seiberg N and Witten E 1994 Nucl. Phys. B 430 485 (erratum) (Preprint hep-th/9407087)
86. Seiberg N and Witten E 1994 Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory Nucl. Phys. B 426 19 Seiberg N and Witten E 1994 Nucl. Phys. B 430 485 (erratum) (Preprint hep-th/9407087)
87. Eguchi T and Kawai H 1982 Reduction of dynamical degrees of freedom in the large N gauge theory Phys. Rev. Lett. 48 1063
88. Weinberg S 1966 Pion scattering lengths Phys. Rev. Lett. 17 616
89. Gasser J and Leutwyler H 1987 Light quarks at low temperatures Phys. Lett. B 184 83
90. Shuryak E V and Verbaarschot J J 1993 Random matrix theory and spectral sum rules for the Dirac operator in QCD Nucl. Phys. A 560 306 (Preprint hep-th/9212088)
91. Verbaarschot J J 1994 The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way Phys. Rev. Lett. 72 2531 (Preprint hep-th/9401059)
92. Gade R 1993 Anderson localization for sublattice models Nucl Phys. B 398 398
93. Forrester P J 1993 The spectrum edge of random matrix ensembles Nucl. Phys. B 402 709
94. Verbaarschot J J and Wettig T 2000 Random matrix theory and chiral symmetry in QCD Annu. Rev. Nucl. Part. Sci. 50 343 (Preprint hep-ph/0003017)
95. Oppermann R 1990 Anderson localization problems in gapless superconducting phases Physica A 167 301
96. Altland A and Zirnbauer M R 1996 Random matrix theory of a chaotic Andreev quantum dot Phys. Rev. Lett. 76 3420
97. Dyson F J 1970 Correlations between the eigenvalues of a random matrix Commun. Math. Phys. 19 235
98. Zirnbauer M R 1996 Riemannian symmetric superspaces and their origin in random-matrix theory J. Math. Phys. 37 4986
99. Kazakov V A and Migdal A A 1993 Induced QCD at large N Nucl. Phys. B 397 214 (Preprint hep-th/9206015)
100. Dijkgraaf R and Vafa C 2002 Matrix models, topological strings, and supersymmetric gauge theories Nucl. Phys. B 644 3 (Preprint hep-th/0206255)
101. David F 1985 Planar diagrams, two-dimensional lattice gravity and surface models Nucl. Phys. B 257 45
102. Kazakov V A, Migdal A A and Kostov I K 1985 Critical properties of randomly triangulated planar random surfaces Phys. Lett. B 157 295
103. Douglas M R and Shenker S H 1990 Strings in less than one-dimension Nucl. Phys. B 335 635
104. Brezin E and Kazakov V A 1990 Exactly solvable field theories of closed strings Phys. Lett. B 236 144
105. Gross D J and Migdal A A 1990 Nonperturbative two-dimensional quantum gravity Phys. Rev. Lett. 64 127
106. Ambjorn J, Jurkiewicz J and Makeenko Y M 1990 Multiloop correlators for two-dimensional quantum gravity Phys. Lett. B 251 517
107. Bowick M J and Brezin E 1991 Universal scaling of the tail of the density of eigenvalues in random matrix models Phys. Lett. B 268 21
108. Akemann G, Damgaard P H, Magnea U and Nishigaki S 1997 Universality of random matrices in the microscopic limit and the Dirac operator spectrum Nucl. Phys. B 487 721 (Preprint hep-th/9609174)
109. Douglas M R 1990 Strings in less than one-dimension and the generalized K-D-V hierarchies Phys. Lett. B 238 176
110. Dijkgraaf R, Verlinde H and Verlinde E 1991 Loop equations and Virasoro constraints in nonperturbative 2-d quantum gravity Nucl. Phys. B 348 435
111. Di Francesco P, Ginsparg P and Zinn-Justin J 1995 2-D Gravity and random matrices Phys. Rep. 254 l (Preprint hep-th/9306153)
112. Jimbo M, Miwa T, Môri Y and Sato M 1980 Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent Physica D 1 80
113. Tracy C A and Widom H 1994 Level spacing distributions and the Airy kernel Commun. Math. Phys. 159 151
114. Baik J, Deift P and Johannsson K 1999 On the distribution of the length of the longest increasing subsequence of random permutations J. Am. Math. Soc. 36 1119
115. Prähofer M and Spohn H 2000 Universal distributions for growth processes in one dimension and random matrices Phys. Rev. Lett. 84 4882
116. Johansson K 2002 Non-intersecting paths, random tilings and random matrices Prob. Theory Rev. Fields 123 225
117. Zaslavsky G M 1981 Stochasticity in quantum systems Phys. Rep. 80 157
118. Berry M V 1981 Quantizing a classically ergodic system: Sinai's billiard and the KKR method Ann. Phys., NY 13 1163
119. Bohigas O, Giannoni M J and Schmit C 1984 Characterization of chaotic quantum spectra and universality of level fluctuation laws Phys. Rev. Lett. 52 1
120. Sinai Ya G 1970 Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards Russ. Math. Surv. 25 137
121. Haller E, Koppel H and Cederbaum L S 1984 Uncovering the transition from regularity to irregularity in a quantum system Phys. Rev. Lett. 52 1665
122. Seligman T, Verbaarschot J J M and Zirnbauer M R 1984 Quantum chaos and the transition from chaotic to regular motion Phys. Rev. Lett. 53 215
123. Berry M V 1985 Semiclassical theory of spectral rigidity Proc. R. Soc. A 400 229
124. Bogomolny E B and Keating J P 1996 Gutzwiller's trace formula and spectral statistics Phys. Rev. Lett. 77 1472
125. Haake F 1999 Quantum Signatures of Chaos 2nd edn (Berlin: Springer)
126. Stoeckmann H-J 1999 Quantum Chaos: An Introduction (Cambridge: Cambridge University Press)
127. Laloux L, Cizeau P, Bouchard J-P and Potters M 1999 Noise dressing of financial correlation matrices Phys. Rev. Lett. 83 1467
128. Plerou V, Gopikrishnan P, Rosnow B, Nunes Amaral L A and Stanley H E 1999 Universal and nonuniversal properties of cross correlations in financial time series Phys. Rev. Lett. 83 1471
129. Moustakas A L, Baranger H U, Balents L, Sengupta A M and Simon S H 2000 Communication through a diffusive medium: coherence and capacity Science 287 287 (Preprint cond-mat/0009097)