Moderate deviations for extreme eigenvalues of beta-Laguerre ensembles

被引：3

作者：

Chen, Lei ^{[1
]}

Wang, Shaochen ^{[2
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou, Jiangsu, Peoples R China

[2] South China Univ Technol, Sch Math, Guangzhou, Peoples R China

来源：

RANDOM MATRICES-THEORY AND APPLICATIONS | 2020年 / 9卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Beta-Laguerre ensembles; extreme eigenvalues; moderate deviations; random matrices; FLUCTUATIONS; SPECTRUM; HERMITE;

D O I：

10.1142/S2010326320500033

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Let lambda(max), lambda(min) be respectively the largest and smallest eigenvalues of beta-Laguerre ensembles with parameters (n, p, beta). For fixed beta > 0, under the condition that p is much larger than n(log n)(2), we obtain the full moderate deviation principles for lambda(max) and lambda(min) by using the asymptotic expansion technique. Interestingly, under this regime, our results show that asymptotically the exponential tails of the extreme eigenvalues are Gaussian-type distribution tail rather than the Tracy-Widom-type distribution tail.

引用

页数：20