Large n limit of Gaussian random matrices with external source, part I

Communications in Mathematical Physics

Volumn 252, Issue 1-3, 2004, Pages 43-76

  Bleher, Pavel ^a   Kuijlaars, Arno B J ^b  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11244356563     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1196-2     Document Type: Article

References (31)

1. Aptekarev, A.I.: Multiple orthogonal polynomials. J. Comput. Appl. Math. 99, 423-447 (1998)
2. Aptekarev, A.I., Bleher, P.M., Kuijlaars, A.B.J.: Large n limit of Gaussian random matrices with external source part II. math-ph/0408041
3. Aptekarev, A.I., Branquinho, A., Van Assche, W.: Multiple orthogonal polynomials for classical weights. Trans. Amer. Math. Soc. 355, 3887-3914 (2003)
4. Aptekarev, A.I., Stahl, H.: Asymptotics of Hermite-Padé polynomials. In: Progress in Approximation Theory. A.A. Gonchar, E.B. Saff (eds). New York: Springer-Verlag, 1992, pp. 27-167
5. Bleher, P., Its, A.: Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and the universality in the matrix model. Ann. Math. 150, 185-266 (1999)
6. Bleher, P., Its, A.: Double scaling limit in the random matrix model. The Riemann-Hilbert approach. Commun. Pure Appl. Math. 56, 433-516 (2003)
7. Bleher, P.M., Kuijlaars, A.B.J.: Random matrices with external source and multiple orthogonal polynomials. Int. Math. Research Notices 2004(3), 109-129 (2004)
8. Bleher, P.M., Kuijlaars, A.B.J.: Integral representations for multiple Hermite and multiple Laguerre polynomials. math.CA/0406616
9. Brézin, E., Hikami, S.: Spectral form factor in a random matrix theory. Phys. Rev. E 55, 4067-4083 (1997)
10. Brézin, E., Hikami, S.: Correlations of nearby levels induced by a random potential. Nucl. Phys. B 479, 697-706 (1996)
11. Brézin, E., Hikami, S.: Extension of level spacing universality. Phys. Rev. E 56, 264-269 (1997)
12. Brézin, E., Hikami, S.: Universal singularity at the closure of a gap in a random matrix theory. Phys. Rev. E 57, 4140-4149 (1998)
13. Brézin, E., Hikami, S.: Level spacing of random matrices in an external source. Phys. Rev. E 58, 7176-7185 (1998)
14. Deift, P.: Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert approach. Courant Lecture Notes in Mathematics, Vol. 3, Providence R.I.: Amer. Math. Soc., 1999
15. Deift, P., Kriecherbauer, T., McLaughlin, K.T.-R., Venakides, S., Zhou, X.: Uniform asymptotics of polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Commun. Pure Appl. Math. 52, 1335-1425 (1999)
16. Deift, P., Kriecherbauer, T., McLaughlin, K.T.-R., Venakides, S., Zhou, X.: Strong asymptotics of orthogonal polynomials with respect to exponential weights. Commun. Pure Appl. Math 52, 1491-1552 (1999)
17. Deift, P., Zhou, X.: A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation. Ann. Math. 137, 295-368 (1993)
18. Dyson, F.J.: Correlations between eigenvalues of a random matrix. Commun. Math. Phys 19, 235-250 (1970)
19. Gonchar, A.A., Rakhmanov, E.A.: On the convergence of simultaneous Padé approximants for systems of functions of Markov type (Russian). Trudy Mat. Inst. Steklov 157, 31-48 (1981); English transl. in Proc. Steklov Math. Inst. 3, 31-50 (1983)
20. Gonchar, A.A., Rakhmanov, E.A.: On the convergence of simultaneous Padé approximants for systems of functions of Markov type (Russian). Trudy Mat. Inst. Steklov 157, 31-48 (1981); English transl. in Proc. Steklov Math. Inst. 3, 31-50 (1983)
21. Kuijlaars, A.B.J.: Riemann-Hilbert analysis for orthogonal polynomials. In: Orthogonal Polynomials and Special Functions, E. Koelink, W. Van Assche, (eds), Lecture Notes in Mathematics, Vol. 1817, Berlin-Heidelberg-New York: Springer-Verlag, 2003, pp. 167-210
22. Kuijlaars, A.B.J., McLaughlin, K.T.-R.: Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields. Commun. Pure Appl. Math. 53, 736-785 (2000)
23. Kuijlaars, A.B.J., Van Assche, W., Wielonsky, F.: Quadratic Hermite-Padé approximation to the exponential function: a Riemann-Hilbert approach. math.CA/0302357, to appear in Constr. Approx
24. Mehta, M.L.: Random Matrices. 2nd edition, Boston: Academic Press, 1991
25. Nikishin, E.M., Sorokin, V.N.: Rational Approximations and Orthogonality. Transl. Math. Monogr.: Providence R.I. 92, Amer. Math. Soc., 1991
26. Nuttall, J.: Asymptotics of diagonal Hermite-Padé polynomials. J. Approx. Theory 42, 299-386 (1984)
27. Pastur, L.A.: The spectrum of random matrices (Russian). Teoret. Mat. Fiz. 10, 102-112 (1972)
28. Van Assche, W., Coussement, E.: Some classical multiple orthogonal polynomials. J. Comput. Appl. Math. 127, 317-347 (2001)
29. Van Assche, W., Geronimo, J., Kuijlaars, A.B.J.: Riemann-Hilbert problems for multiple orthogonal polynomials. In: Special Functions 2000: Current Perspectives and Future Directions, J. Bustoz, et al. (eds), Dordrecht, Kluwer, 2001. pp. 23-59
30. Zinn-Justin, P.: Random Hermitian matrices in an external field. Nucl. Phys. B 497, 725-732 (1997)
31. Zinn-Justin, P.: Universality of correlation functions of Hermitian random matrices in an external field. Commun. Math. Phys. 194, 631-650 (1998)