CORRELATED RANDOM MATRICES: BAND RIGIDITY AND EDGE UNIVERSALITY

被引：24

作者：

Alt, Johannes ^{[1
]}

Erdos, Laszlo ^{[2
]}

Krueger, Torben ^{[3
]}

Schroeder, Dominik ^{[2
]}

机构：

[1] Univ Geneva, Geneva, Switzerland

[2] IST Austria, Klosterneuburg, Austria

[3] Univ Bonn, Bonn, Germany

来源：

ANNALS OF PROBABILITY | 2020年 / 48卷 / 02期

基金：

欧洲研究理事会;

关键词：

Local law; spectral universality; Tracy-Widom distribution; SPECTRAL STATISTICS; GENERALIZED WIGNER; LOCAL STATISTICS; EIGENVALUE; CONVERGENCE;

D O I：

10.1214/19-AOP1379

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 prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.

引用

页码：963 / 1001

页数：39

共 50 条

[1] Edge universality of correlated Gaussians [J].