Edge universality for orthogonal ensembles of random matrices

Journal of Statistical Physics

Volumn 136, Issue 1, 2009, Pages 35-50

  Shcherbina, M ^a  

^a B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

Author keywords

Orthogonal ensembles; Random matrices; Universality

Indexed keywords

EID: 70349306388     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9766-5     Document Type: Article

References (25)

1. Albeverio, S., Pastur, L., Shcherbina, M.: On asymptotic properties of the Jacobi matrix coefficients. Mat. Fiz. Anal. Geom. 4, 263-277 (1997)
2. Albeverio, S., Pastur, L., Shcherbina, M.: On the 1/n expansion for some unitary invariant ensembles of random matrices. Commun. Math. Phys. 224, 271-305 (2001)
3. Boutet de Monvel, A., Pastur, L., Shcherbina, M.: On the statistical mechanics approach in the random matrix theory. Integrated density of states. J. Stat. Phys. 79, 585-611 (1995)
4. Claeys, T., Kuijalaars, A.B.J.: Universality of the double scaling limit in random matrix models. Commun. Pure Appl. Math. 59, 1573-1603 (2006)
5. Deift, P., Gioev, D.: Universality in random matrix theory for orthogonal and symplectic ensembles. Int. Math. Res. Pap. 2007, 004-116
6. Deift, P., Gioev, D.: Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices. Commun. Pure Appl. Math. 60, 867-910 (2007)
7. Deift, P., Kriecherbauer, T., McLaughlin, K., Venakides, S., Zhou, X.: 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, 1335-1425 (1999)
8. Deift, P., Gioev, D., Kriecherbauer, T., Vanlessen, M.: Universality for orthogonal and symplectic Laguerre-type ensembles. J. Stat. Phys. 129, 949-1053 (2007)
9. Dyson, D.J.: A Class of Matrix Ensembles. J. Math. Phys. 13, 90-107 (1972)
10. Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators. AMS, Providence (1969)
11. Johansson, K.: On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J. 91, 151-204 (1998)
12. Levin, L., Lubinskky, D.S.: Universality limits in the bulk for varying measures. Adv. Math. 219, 743-779 (2008)
13. Mehta, M.L.: Random Matrices. Academic Press, New York (1991)
14. Pastur, L., Shcherbina, M.: Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J. Stat. Phys. 86, 109-147 (1997)
15. Pastur, L., Shcherbina, M.: On the edge universality of the local eigenvalue statistics of matrix models. Mat. Fiz. Anal. Geom. 10(3), 335-365 (2003)
16. Pastur, L., Shcherbina, M.: Bulk universality and related properties of Hermitian matrix models. J. Stat. Phys. 130, 205-250 (2007)
17. Saff, E., Totik, V.: Logarithmic Potentials with External Fields. Springer, Berlin (1997)
18. Shcherbina, M.: Double scaling limit for matrix models with non analytic potentials. J. Math. Phys. 49, 033501-033535 (2008)
19. Shcherbina, M.: On universality for orthogonal ensembles of random matrices. Commun. Math. Phys. 285, 957-974 (2009)
20. Stojanovic, A.: Universality in orthogonal and symplectic invariant matrix models with quatric potentials. Math. Phys. Anal. Geom. 3, 339-373 (2002)
21. Stojanovic, A.: Universalité pour des modéles orthogonale ou symplectiqua et a potentiel quartic. Math. Phys. Anal. Geom. Preprint Bibos 02-07-98
22. Tracy, C.A., Widom, H.: Level spacing distributions and the Airy kernel. Commun. Math. Phys. 159, 151-174 (1994)
23. Tracy, C.A., Widom, H.: Correlation functions, cluster functions, and spacing distributions for random matrices. J. Stat. Phys. 92, 809-835 (1998)
24. Tracy, C.A., Widom, H.: Matrix Kernels for the Gaussian orthogonal and symplectic ensembles. Ann. Inst. Fourier (Grenoble) 55, 2197-2207 (2005)
25. Widom, H.: On the relations between orthogonal, symplectic and unitary matrix models. J. Stat. Phys. 94, 347-363 (1999)