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
topReferences
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