@article{AIHPB_2003__39_6_1013_0, author = {Dembo, A. and Guionnet, Alice and Zeitouni, Ofer}, title = {Moderate deviations for the spectral measure of certain random matrices}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {39}, year = {2003}, pages = {1013-1042}, doi = {10.1016/S0246-0203(03)00024-4}, mrnumber = {2010395}, zbl = {1038.60027}, language = {en}, url = {http://dml.mathdoc.fr/item/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) pp. 1013-1042. doi : 10.1016/S0246-0203(03)00024-4. http://gdmltest.u-ga.fr/item/AIHPB_2003__39_6_1013_0/
[1] Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields 108 (1997) 517-542. | MR 1465640 | Zbl 0954.60029
, ,[2] On the free convolution with semi-circular distribution, Indiana Univ. Math. J. 46 (1997) 705-718. | MR 1488333 | Zbl 0904.46045
,[3] Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, Probab. Theory Related Fields 112 (1998) 373-409. | MR 1660906 | Zbl 0919.60056
, ,[4] Free diffusions, free entropy and free Fisher information, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 581-606. | Numdam | MR 1851716 | Zbl 1020.46018
, ,[5] Fluctuations de la loi empirique des grandes matrices aléatoires, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 373-402. | Numdam | MR 1831988 | Zbl 1016.15020
,[6] Large deviations upper bounds and non-commutative entropies for some matrices ensembles, Ann. Probab. 29 (2001) 1205-1261. | MR 1872742 | Zbl 1022.60026
, ,[7] T. Cabanal-Duvillard, A. Guionnet, Discussion around non-commutative entropies, Adv. Math. (2002), submitted for publication.
[8] Large Deviations Techniques and Applications, Springer, New York, 1998. | MR 1619036 | Zbl 0896.60013
, ,[9] 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 1899457 | Zbl 0995.60028
,[10] A. Guionnet, First order asymptotic of matrix integrals; a rigorous approach towards the understanding of matrix models, Preprint, 2002. | MR 2034487
[11] Concentration of the spectral measure for large matrices, Electron. Comm. Probab. 5 (2000) 119-136. | MR 1781846 | Zbl 0969.15010
, ,[12] Large deviation asymptotics for spherical integrals, J. Funct. Anal. 188 (2002) 461-515. | MR 1883414 | Zbl 1002.60021
, ,[13] Asymptotic fluctuations of a particle system with singular interaction, Stochastic Process. Appl. 93 (2001) 25-56. | MR 1819483 | Zbl 1053.60104
,[14] On fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J. 91 (1998) 151-204. | MR 1487983 | Zbl 1039.82504
,[15] Hydrodynamics and large deviation for simple exclusion processes, Comm. Pure Appl. Math. 42 (1989) 115-137. | MR 978701 | Zbl 0644.76001
, , ,[16] Random Matrices, Academic Press, 1991. | MR 1083764 | Zbl 0780.60014
,[17] The method of stochastic exponentials for large deviations, Stochastic Process. Appl. 54 (1994) 45-70. | MR 1302694 | Zbl 0812.60026
,[18] Integral Equations, Interscience, 1970. | Zbl 0078.09404
,[19] Lectures on free probability theory, in: Lecture Notes in Math., 1738, 2000, pp. 283-349. | MR 1775641 | Zbl 1015.46037
,[20] On the distribution of the roots of certain symmetric matrices, Ann. Math. 67 (1958) 325-327. | MR 95527 | Zbl 0085.13203
,[21] Large deviations, moderate deviations and LIL for empirical processes, Ann. Probab. 22 (1994) 17-27. | MR 1258864 | Zbl 0793.60032
,