Edge universality for non-Hermitian random matrices

被引：29

作者：

Cipolloni, Giorgio ^{[1
]}

Erdos, Laszlo ^{[1
]}

Schroeder, Dominik ^{[2
]}

机构：

[1] IST Austria, Campus 1, A-3400 Klosterneuburg, Austria

[2] Swiss Fed Inst Technol, Inst Theoret Studies, Clausiusstr 47, CH-8092 Zurich, Switzerland

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2021年 / 179卷 / 1-2期

关键词：

Ginibre ensemble; Universality; Circular law; Girko's formula; EIGENVALUE STATISTICS; BULK UNIVERSALITY; SPECTRAL-RADIUS; REAL; ENSEMBLES; DISTRIBUTIONS;

D O I：

10.1007/s00440-020-01003-7

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 consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.

引用

页码：1 / 28

页数：28

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