Moderate deviations for the spectral measure of certain random matrices
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 6, pp. 1013-1042. 
@article{AIHPB_2003__39_6_1013_0,
     author = {Dembo, A. and Guionnet, A. and Zeitouni, O.},
     title = {Moderate deviations for the spectral measure of certain random matrices},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1013--1042},
     publisher = {Elsevier},
     volume = {39},
     number = {6},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00024-4},
     mrnumber = {2010395},
     zbl = {1038.60027},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(03)00024-4/}
}
TY  - JOUR
AU  - Dembo, A.
AU  - Guionnet, A.
AU  - Zeitouni, O.
TI  - Moderate deviations for the spectral measure of certain random matrices
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2003
SP  - 1013
EP  - 1042
VL  - 39
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S0246-0203(03)00024-4/
DO  - 10.1016/S0246-0203(03)00024-4
LA  - en
ID  - AIHPB_2003__39_6_1013_0
ER  - 
%0 Journal Article
%A Dembo, A.
%A Guionnet, A.
%A Zeitouni, O.
%T Moderate deviations for the spectral measure of certain random matrices
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2003
%P 1013-1042
%V 39
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S0246-0203(03)00024-4/
%R 10.1016/S0246-0203(03)00024-4
%G en
%F AIHPB_2003__39_6_1013_0
Dembo, A.; Guionnet, A.; Zeitouni, O. Moderate deviations for the spectral measure of certain random matrices. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 6, pp. 1013-1042. doi : 10.1016/S0246-0203(03)00024-4. http://www.numdam.org/articles/10.1016/S0246-0203(03)00024-4/

[1] G. Ben Arous, A. Guionnet, Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields 108 (1997) 517-542. | MR | Zbl

[2] P. Biane, On the free convolution with semi-circular distribution, Indiana Univ. Math. J. 46 (1997) 705-718. | MR | Zbl

[3] P. Biane, R. Speicher, Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, Probab. Theory Related Fields 112 (1998) 373-409. | MR | Zbl

[4] P. Biane, R. Speicher, Free diffusions, free entropy and free Fisher information, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 581-606. | Numdam | MR | Zbl

[5] T. Cabanal-Duvillard, Fluctuations de la loi empirique des grandes matrices aléatoires, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 373-402. | Numdam | MR | Zbl

[6] T. Cabanal-Duvillard, A. Guionnet, Large deviations upper bounds and non-commutative entropies for some matrices ensembles, Ann. Probab. 29 (2001) 1205-1261. | MR | Zbl

[7] T. Cabanal-Duvillard, A. Guionnet, Discussion around non-commutative entropies, Adv. Math. (2002), submitted for publication.

[8] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998. | MR | Zbl

[9] A. Guionnet, 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. | Numdam | MR | Zbl

[10] A. Guionnet, First order asymptotic of matrix integrals; a rigorous approach towards the understanding of matrix models, Preprint, 2002. | MR

[11] A. Guionnet, O. Zeitouni, Concentration of the spectral measure for large matrices, Electron. Comm. Probab. 5 (2000) 119-136. | MR | Zbl

[12] A. Guionnet, O. Zeitouni, Large deviation asymptotics for spherical integrals, J. Funct. Anal. 188 (2002) 461-515. | MR | Zbl

[13] S. Israelsson, Asymptotic fluctuations of a particle system with singular interaction, Stochastic Process. Appl. 93 (2001) 25-56. | MR | Zbl

[14] K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J. 91 (1998) 151-204. | MR | Zbl

[15] C. Kipnis, S. Olla, S.R.S. Varadhan, Hydrodynamics and large deviation for simple exclusion processes, Comm. Pure Appl. Math. 42 (1989) 115-137. | MR | Zbl

[16] M.L. Mehta, Random Matrices, Academic Press, 1991. | MR | Zbl

[17] A. Puhalskii, The method of stochastic exponentials for large deviations, Stochastic Process. Appl. 54 (1994) 45-70. | MR | Zbl

[18] F. Tricomi, Integral Equations, Interscience, 1970. | Zbl

[19] D. Voiculescu, Lectures on free probability theory, in: Lecture Notes in Math., 1738, 2000, pp. 283-349. | MR | Zbl

[20] E. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. Math. 67 (1958) 325-327. | MR | Zbl

[21] L.-M. Wu, Large deviations, moderate deviations and LIL for empirical processes, Ann. Probab. 22 (1994) 17-27. | MR | Zbl

Cité par Sources :