Large Deviations for the Largest Eigenvalue of Sub-Gaussian Matrices

被引：12

作者：

Augeri, Fanny ^{[1
]}

Guionnet, Alice ^{[2
]}

Husson, Jonathan ^{[2
]}

机构：

[1] Weizmann Inst Sci, 234 Herzl St, IL-7610001 Rehovot, Israel

[2] Ecole Normale Super Lyon, 46 Allee Italie, F-69364 Lyon, France

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2021年 / 383卷 / 02期

基金：

欧洲研究理事会;

关键词：

D O I：

10.1007/s00220-021-04027-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish large deviations estimates for the largest eigenvalue of Wigner matrices with sub-Gaussian entries. Under technical assumptions, we show that the large deviation behavior of the largest eigenvalue is universal for small deviations, in the sense that the speed and the rate function are the same as in the case of the GOE. In contrast, in the regime of very large deviations, we obtain a non-universal rate function, thus establishing the existence of a transition between two different large deviation mechanisms.

引用

页码：997 / 1050

页数：54

共 23 条

[1]

Anderson G. W., 2010, Cambridge Studies in Advanced Mathematics, V118

[2]

[Anonymous], 2018, ARXIV180911148

[3]

Augeri, 2019, ARXIV191110591

[4] Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails [J].