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

Communications in Mathematical Physics

Volumn 259, Issue 2, 2005, Pages 367-389

  Aptekarev, Alexander I ^a   Bleher, Pavel M ^b   Kuijlaars, Arno B J ^c  

^a KELDYSH INSTITUTE OF APPLIED MATHEMATICS   (Russian Federation)

^b INDIANA UNIVERSITY   (United States)

^c UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24144459114     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1367-9     Document Type: Article

References (34)

1. Aptekarev, A.I., Branquinho, A., Van Assche, W.: Multiple orthogonal polynomials for classical weights. Trans. Amer. Math. Soc. 355, 3887-3914 (2003)
2. Baik, J.: Random vicious walks and random matrices. Commun. Pure Appl. Math. 53, 1385-1410 (2000)
3. 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)
4. Bleher, P., Its, A.: Double scaling limit in the random matrix model. The Riemann-Hilbert approach. Commun. Pure Appl. Math. 56, 433-516 (2003)
5. Bleher, P.M., Kuijlaars, A.B.J.: Random matrices with external source and multiple orthogonal polynomials. Internat. Math. Research Notices 2004, 3, 109-129 (2004)
6. Bleher, P.M., Kuijlaars, A.B.J.: Large n limit of Gaussian random matrices with external source. Part I. Commun. Math. Phys. 252, 43-76 (2004)
7. Bleher, P.M., Kuijlaars, A.B.J.: Integral representations for multiple Hermite and multiple Laguerre polynomials. http://arxiv.org/abs/math.CA/0406616, 2004 to appear in Annales de l'Institut Fourier
8. Bleher, P.M., Kuijlaars, A.B.J.: Large n limit of Gaussian random matrices with external source, Part III: double scaling limit in the critical case. In preparation
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. Daems, E., Kuijlaars, A.B.J.: A Christoffel-Darboux formula for multiple orthogonal polynomials. J. Approx. Theory 130, 190-202 (2004)
15. 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
16. 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)
17. 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)
18. Deift, P., Zhou, X.: A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation. Ann. Math. 137, 295-368 (1993)
19. Itzykson, C., Zuber, J.B.: The planar approximation II. J. Math. Phys. 21, 411-421 (1980)
20. Johansson, K.: Non-intersecting paths, random tilings and random matrices. Probab. Theo Related Fields 123, 225-280 (2002)
21. Karlin, S., McGregor, J.: Coincidence probabilities. Pacific J. Math. 9, 1141-1164 (1959)
22. Katori, M., Tanemura, H.: Scaling limit of vicious walks and two-matrix model. Phys. Rev. E 66, Art. No. 011105 (2002)
23. 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-Heiderberg-New York, Springer-Verlag, 2003, pp. 167-210
24. Kuijlaars, A.B.J., Van Assche, W., Wielonsky, F.: Quadratic Hermite-Padápproximation to the exponential function: a Riemann-Hilbert approach. http://Constr.org/list/math.CA/0302357, 2003 Approx. 21, 351-412 (2005)
25. Kuijlaars, A.B.J., Vanlessen, M.: Universality for eigenvalue correlations from the modified Jacobi unitary ensemble. Internat. Math. Research Notices 2002, 1575-1600 (2002)
26. Kuijlaars, A.B.J., Vanlessen, M.: Universality for eigenvalue correlations at the origin of the spectrum. Commun. Math. Phys. 243, 163-191 (2003)
27. Mehta, M.L.: Random Matrices. 2nd edition, Boston: Academic Press, 1991
28. Nagao, T., Forrester, P.J.: Vicious random walkers and a discretization of Gaussian random matrix ensembles. Nuclear Phys. B 620, 551-565 (2002)
29. Pastur, L.A.: The spectrum of random matrices (Russian). Teoret. Mat. Fiz. 10, 102-112 (1972)
30. Tracy, C.A., Widom, H.: The Pearcey process. http://arxiv.org/abs/math. PR/0412005, 2004
31. Van Assche, W., Coussement, E.: Some classical multiple orthogonal polynomials. J. Comput. Appl. Math. 127, 317-347 (2001)
32. Van Assche, W., Geronimo, J.S., 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
33. Zinn-Justin, P.: Random Hermitian matrices in an external field. Nucl. Phys. B 497, 725-732 (1997)
34. Zinn-Justin, P.: Universality of correlation functions of Hermitian random matrices in an external field. Commun. Math. Phys. 194, 631-650 (1998)