Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices

Communications in Mathematical Physics

Volumn 215, Issue 3, 2001, Pages 683-705

  Johansson, Kurt ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035530553     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000328     Document Type: Article

References (31)

1. 1. Andréief, C.: Note sur une relation les integrales définies des produits de fonctions. Mém. de la Soc. Bordeaux, 2, 1-14 (1883)
2. 2. Bai, Z.D.: Methodologies in spectral analysis of large dimensional random matrices: A review. Statistica Sinica 9, 611-661 (1999)
3. 3. Bleher, P., Its, A.: Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. Math. 150, 185-266 (1999)
4. 4. Borodin, A.: Biorthogonal ensembles. Nucl. Phys. B 536, 704-732 (1999)
5. 5. Brézin, E., Hikami, S.: Correlations of nearby levels induced by a random potential. Nucl. Phys. B 479, 697-706 (1996)
6. 6. Brézin, E., Hikami, S.: Spectral form factor in a random matrix theory. Phys. Rev. E 55, 4067-4083 (1997)
7. 7. Brézin, E., Hikami, S.: An extension of level-spacing universality. cond-mat/9702213
8. 8. Deift, P., Kriecherbauer, T., McLaughlin, K.T.-R., Venakides, S., Zhou, X.: Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure. Appl. Math. 52, 1335-1425 (1999)
9. 9. Dyson, F.J.: A Brownian-motion Model for the Eigenvalues of a Random Matrix. J. Math. Phys. 3, 1191-1198 (1962)
10. 10. Grabiner, D.J.: Brownian motion in a Weyl chamber, non-colliding particles and random matrices. Ann. Inst. H. Poincaré 35, 177-204 (1999)
11. 11. Guionnet, A., Zeitouni, O.: Concentration of the spectral measure for large matrices. Preprint (2000)
12. 12. Harish-Chandra, Differential operators on a semisimple Lie algebra. Amer. J. Math. 79, 87-120 (1957)
13. 13. Hobson, D.G., Werner, W.: Non-colliding Brownian motions on the circle. Bull. London Math. Soc. 28, 543-650 (1996)
14. 14. Itzykson, C., Zuber, J.-B.: The planar approximation II. J. Math. Phys., 21, 411-421 (1980)
15. 15. Johansson, K.: Random growth and Random matrices. To appear in the Proceedings of the third European Congress of Mathematics
16. 16. Johansson, K.: Non-intersecting paths, random tilings and random matrices. In preparation
17. 17. Karlin, S., McGregor, G.: Coincidence probabilities. Pacific J. Math, 9, 1141-1164 (1959)
18. 18. Katz, N.M., Sarnak, P.: Random Matrices, Frobenius Eigenvalues and Monodromy. AMS Colloquium Publications, Vol. 45, 1999
19. 19. Khorunzhy, A.: On smoothed density of states for Wigner random matrices. Random Oper. and Stoch. Equ. 5, 147-162 (1997)
20. 20. Khorunzhy, A., Khoruzhenko, B.A., Pastur, L.A.: On asymptotic properties of large random matrices with independent entries. J. Math. Phys. 37, 5033-5060 (1996)
21. 21. Mehta, M.L.: Random Matrices. 2nd ed., San Diego: Academic Press, 1991
22. 22. Okounkov, A.: Infinite wedge and measures on partitions. math.RT/9907127
23. 23. Pastur, L.A., Shcherbina, M.: Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J. Stat. Phys. 86, 109-147 (1997)
24. 24. Pauwels, E.J., Rogers, L.G.G.: Skew-product decompositions of Brownian motions. In: Geometry of Random Motion, R. Durrett, M. A. Pinsky, eds., Providence, RI: AMS Contemporary Mathematics, Vol. 73, 1988
25. 25. Pinsky, R.G.: On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes. Ann. Prob. 13, 363-378 (1985)
26. 26. Porter, C.E., ed.: Statistical Theories of spectra: Fluctuations. New York: Academic Press, 1965
27. 27. Rains, E.: Correlation functions for symmetrized increasing subsequences. math.CO/0006097 (2000)
28. 28. Soshnikov, A.: Universality at the edge of the spectrum in Wigner random matrices. Commun. Math. Phys. 207, 697-733 (1999)
29. 29. Sinai, Ya., Soshnikov, A.: Central limit theorem for traces of large random symmetric matrices with independent matrix elements. Bol. Soc. Brasil. Mat. 29, 1-24 (1998)
30. 30. Sinai, Ya., Soshnikov, A.: A refinment of Wigner's semicircle law in a neighborhood of the spectrum edge for symmetric matrices. Funct. Anal. Appl. 32, 114-131 (1998)
31. 31. Tracy, C.A., Widom, H.: Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices. J. Statist. Phys. 92, 809-835 (1998)