Small deviations for beta ensembles

被引：66

作者：

Ledoux, Michel ^{[1
]}

Rider, Brian ^{[2
]}

机构：

[1] Univ Toulouse, Inst Math Toulouse, F-31062 Toulouse, France

[2] Univ Colorado, Dept Math, Boulder, CO 80309 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

基金：

美国国家科学基金会;

关键词：

Random matrices; eigenvalues; small deviations; DISTRIBUTIONS; EIGENVALUE; INEQUALITIES; MATRICES; EDGE;

D O I：

10.1214/EJP.v15-798

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish various small deviation inequalities for the extremal (soft edge) eigenvalues in the beta-Hermite and beta-Laguerre ensembles. In both settings, upper bounds on the variance of the largest eigenvalue of the anticipated order follow immediately.

引用

页码：1319 / 1343

页数：25

共 50 条

[41] Unilateral small deviations of processes related to the fractional Brownian motion
Molchan, G.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2008, 118 (11) : 2085 - 2097
[42] Small deviations of Gaussian random fields in Lq-spaces
Lifshits, Mikhail
Linde, Werner
Shi, Zhan
ELECTRONIC JOURNAL OF PROBABILITY, 2006, 11 : 1204 - 1233
[43] Entropy and the Shannon-McMillan-Breiman Theorem for Beta Random Matrix Ensembles
Alexander Bufetov
Sevak Mkrtchyan
Maria Shcherbina
Alexander Soshnikov
Journal of Statistical Physics, 2013, 152 : 1 - 14
[44] Edge of spiked beta ensembles, stochastic Airy semigroups and reflected Brownian motions
Lamarre, Pierre Yves Gaudreau
Shkolnikov, Mykhaylo
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2019, 55 (03): : 1402 - 1438
[45] SMALL DEVIATIONS OF SERIES OF INDEPENDENT NONNEGATIVE RANDOM VARIABLES WITH SMOOTH WEIGHTS
Rozovsky, L. V.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2014, 58 (01) : 121 - 137
[46] Small deviations in L2-norm for Gaussian dependent sequences
Hong, Seok Young
Lifshits, Mikhail
Nazarov, Alexander
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2016, 21
[47] Small Deviations of the Maximal Element of a Sequence of Weighted Independent Random Variables
Rozovskii, L. V.
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2011, 44 (02) : 129 - 133
[48] Moderate deviations and central limit theorem for small perturbation Wishart processes
Lei Chen
Fuqing Gao
Shaochen Wang
Frontiers of Mathematics in China, 2014, 9 : 1 - 15
[49] Moderate deviations and central limit theorem for small perturbation Wishart processes
Chen, Lei
Gao, Fuqing
Wang, Shaochen
FRONTIERS OF MATHEMATICS IN CHINA, 2014, 9 (01) : 1 - 15
[50] Overcoming limitations of modelling rare species by using ensembles of small models
Breiner, Frank T.
Guisan, Antoine
Bergamini, Ariel
Nobis, Michael P.
METHODS IN ECOLOGY AND EVOLUTION, 2015, 6 (10): : 1210 - 1218

← 1 2 3 4 5 →