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

共 59 条

[1] Stability of the matrix Dyson equation and random matrices with correlations [J].

Ajanki, Oskari H. ;

Erdos, Laszlo ;

Krueger, Torben .

PROBABILITY THEORY AND RELATED FIELDS, 2019, 173 (1-2) :293-373

[2] Universality for general Wigner-type matrices [J].

Ajanki, Oskari H. ;

Erdos, Laszlo ;

Krueger, Torben .

PROBABILITY THEORY AND RELATED FIELDS, 2017, 169 (3-4) :667-727

[3] CORRELATED RANDOM MATRICES: BAND RIGIDITY AND EDGE UNIVERSALITY [J].

Alt, Johannes ;

Erdos, Laszlo ;

Krueger, Torben ;

Schroeder, Dominik .

ANNALS OF PROBABILITY, 2020, 48 (02) :963-1001

[4] LOCAL INHOMOGENEOUS CIRCULAR LAW [J].

Alt, Johannes ;

Erdos, Laszlo ;

Krueger, Torben .

ANNALS OF APPLIED PROBABILITY, 2018, 28 (01) :148-203

[5]

[Anonymous], 1994, J. Amer. Math. Soc., DOI DOI 10.1090/S0894-0347-1994-1231689-0

[6] LIMITING BEHAVIOR OF THE NORM OF PRODUCTS OF RANDOM MATRICES AND 2 PROBLEMS OF GEMAN-HWANG [J].

BAI, ZD ;

YIN, YQ .

PROBABILITY THEORY AND RELATED FIELDS, 1986, 73 (04) :555-569

[7]

Bai ZD, 1997, ANN PROBAB, V25, P494

[8] ON THE SPECTRAL RADIUS OF A RANDOM MATRIX: AN UPPER BOUND WITHOUT FOURTH MOMENT [J].

Bordenave, Charles ;

Caputo, Pietro ;

Chafai, Djalil ;

Tikhomirov, Konstantin .

ANNALS OF PROBABILITY, 2018, 46 (04) :2268-2286

[9] Around the circular law [J].

Bordenave, Charles ;

Chafai, Djalil .

PROBABILITY SURVEYS, 2012, 9 :1-89

[10] The Ginibre Ensemble of Real Random Matrices and its Scaling Limits [J].

Borodin, A. ;

Sinclair, C. D. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 291 (01) :177-224

← 1 2 3 4 5 6 →