Functional CLT for non-Hermitian random matrices

被引：1

作者：

Erdos, Laszlo ^{[1
]}

Ji, Hong Chang ^{[1
]}

机构：

[1] IST Austria, Klosterneuburg, Austria

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2023年 / 59卷 / 04期

基金：

欧洲研究理事会;

关键词：

Linear statistics; Central limit theorem; Gaussian free field; LINEAR EIGENVALUE STATISTICS; GAUSSIAN FLUCTUATIONS; CONVERGENCE; ENSEMBLES;

D O I：

10.1214/22-AIHP1304

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：

For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm off on the boundary of the limiting spectrum.

引用

页码：2083 / 2105

页数：23