Moderate deviations for the spectral measure of certain random matrices
A. Dembo; A. Guionnet; O. Zeitouni
Annales de l'I.H.P. Probabilités et statistiques (2003)
- Volume: 39, Issue: 6, page 1013-1042
- ISSN: 0246-0203
Access Full Article
topHow to cite
topDembo, A., Guionnet, A., and Zeitouni, O.. "Moderate deviations for the spectral measure of certain random matrices." Annales de l'I.H.P. Probabilités et statistiques 39.6 (2003): 1013-1042. <http://eudml.org/doc/77786>.
@article{Dembo2003,
author = {Dembo, A., Guionnet, A., Zeitouni, O.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {limit theorems; random matrices},
language = {eng},
number = {6},
pages = {1013-1042},
publisher = {Elsevier},
title = {Moderate deviations for the spectral measure of certain random matrices},
url = {http://eudml.org/doc/77786},
volume = {39},
year = {2003},
}
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
PB - Elsevier
VL - 39
IS - 6
SP - 1013
EP - 1042
LA - eng
KW - limit theorems; random matrices
UR - http://eudml.org/doc/77786
ER -
References
top- [1] G. Ben Arous, A. Guionnet, Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields108 (1997) 517-542. Zbl0954.60029MR1465640
- [2] P. Biane, On the free convolution with semi-circular distribution, Indiana Univ. Math. J.46 (1997) 705-718. Zbl0904.46045MR1488333
- [3] P. Biane, R. Speicher, Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, Probab. Theory Related Fields112 (1998) 373-409. Zbl0919.60056MR1660906
- [4] P. Biane, R. Speicher, Free diffusions, free entropy and free Fisher information, Ann. Inst. H. Poincaré Probab. Statist.37 (2001) 581-606. Zbl1020.46018MR1851716
- [5] T. Cabanal-Duvillard, Fluctuations de la loi empirique des grandes matrices aléatoires, Ann. Inst. H. Poincaré Probab. Statist.37 (2001) 373-402. Zbl1016.15020MR1831988
- [6] T. Cabanal-Duvillard, A. Guionnet, Large deviations upper bounds and non-commutative entropies for some matrices ensembles, Ann. Probab.29 (2001) 1205-1261. Zbl1022.60026MR1872742
- [7] T. Cabanal-Duvillard, A. Guionnet, Discussion around non-commutative entropies, Adv. Math. (2002), submitted for publication. Zbl1038.46053
- [8] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998. Zbl0896.60013MR1619036
- [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. Zbl0995.60028MR1899457
- [10] A. Guionnet, First order asymptotic of matrix integrals; a rigorous approach towards the understanding of matrix models, Preprint, 2002. Zbl1076.82026MR2034487
- [11] A. Guionnet, O. Zeitouni, Concentration of the spectral measure for large matrices, Electron. Comm. Probab.5 (2000) 119-136. Zbl0969.15010MR1781846
- [12] A. Guionnet, O. Zeitouni, Large deviation asymptotics for spherical integrals, J. Funct. Anal.188 (2002) 461-515. Zbl1002.60021MR1883414
- [13] S. Israelsson, Asymptotic fluctuations of a particle system with singular interaction, Stochastic Process. Appl.93 (2001) 25-56. Zbl1053.60104MR1819483
- [14] K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J.91 (1998) 151-204. Zbl1039.82504MR1487983
- [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. Zbl0644.76001MR978701
- [16] M.L. Mehta, Random Matrices, Academic Press, 1991. Zbl0780.60014MR1083764
- [17] A. Puhalskii, The method of stochastic exponentials for large deviations, Stochastic Process. Appl.54 (1994) 45-70. Zbl0812.60026MR1302694
- [18] F. Tricomi, Integral Equations, Interscience, 1970. Zbl0078.09404
- [19] D. Voiculescu, Lectures on free probability theory, in: Lecture Notes in Math., 1738, 2000, pp. 283-349. Zbl1015.46037MR1775641
- [20] E. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. Math.67 (1958) 325-327. Zbl0085.13203MR95527
- [21] L.-M. Wu, Large deviations, moderate deviations and LIL for empirical processes, Ann. Probab.22 (1994) 17-27. Zbl0793.60032MR1258864
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.