Moderate deviations for the spectral measure of certain random matrices

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 39, Issue 6, 2003, Pages 1013-1042

  Dembo, A ^a   Guionnet, A ^b   Zeitouni, O ^c  

^a STANFORD UNIVERSITY   (United States)

^b UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Limit theorems; Random matrices

Indexed keywords

EID: 0141537099     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(03)00024-4     Document Type: Article

References (21)

1. Ben Arous G. Guionnet A. Large deviations for Wigner's law and Voiculescu's non-commutative entropy Probab. Theory Related Fields 108 1997 517-542
2. Biane P. On the free convolution with semi-circular distribution Indiana Univ. Math. J. 46 1997 705-718
3. Biane P. Speicher R. Stochastic calculus with respect to free Brownian motion and analysis on Wigner space Probab. Theory Related Fields 112 1998 373-409
4. Biane P. Speicher R. Free diffusions, free entropy and free Fisher information Ann. Inst. H. Poincaré Probab. Statist. 37 2001 581-606
5. Cabanal-Duvillard T. Fluctuations de la loi empirique des grandes matrices aléatoires Ann. Inst. H. Poincaré Probab. Statist. 37 2001 373-402
6. Cabanal-Duvillard T. Guionnet A. Large deviations upper bounds and non-commutative entropies for some matrices ensembles Ann. Probab. 29 2001 1205-1261
7. T. Cabanal-Duvillard, A. Guionnet, Discussion around non-commutative entropies, Adv. Math. (2002), submitted for publication
8. Dembo A. Zeitouni O. Large Deviations Techniques and Applications Second Edition 1998 Springer New York
9. Guionnet A. Large deviation upper bounds and central limit theorems for band matrices and non-commutative functionnals of Gaussian large random matrices Ann. Inst. H. Poincaré Probab. Statist. 38 2002 341-384
10. A. Guionnet, First order asymptotic of matrix integrals; a rigorous approach towards the understanding of matrix models, Preprint, 2002
11. Guionnet A. Zeitouni O. Concentration of the spectral measure for large matrices Electron. Comm. Probab. 5 2000 119-136
12. Guionnet A. Zeitouni O. Large deviation asymptotics for spherical integrals J. Funct. Anal. 188 2002 461-515
13. Israelsson S. Asymptotic fluctuations of a particle system with singular interaction Stochastic Process. Appl. 93 2001 25-56
14. Johansson K. On fluctuations of eigenvalues of random Hermitian matrices Duke Math. J. 91 1998 151-204
15. Kipnis C. Olla S. Varadhan S.R.S. Hydrodynamics and large deviation for simple exclusion processes Comm. Pure Appl. Math. 42 1989 115-137
16. Mehta M.L. Random Matrices Second Edition 1991 Academic Press
17. Puhalskii A. The method of stochastic exponentials for large deviations Stochastic Process. Appl. 54 1994 45-70
18. Tricomi F. Integral Equations 1970 Interscience
19. Voiculescu D. Lectures on free probability theory Lecture Notes in Math. 1738 2000 283-349
20. Wigner E. On the distribution of the roots of certain symmetric matrices Ann. Math. 67 1958 325-327
21. Wu L.-M. Large deviations, moderate deviations and LIL for empirical processes Ann. Probab. 22 1994 17-27