Semicircle Law for a Matrix Ensemble with Dependent Entries

被引：17

作者：

Hochstaettler, Winfried ^{[1
]}

Kirsch, Werner ^{[1
]}

Warzel, Simone ^{[2
]}

机构：

[1] Fernuniv, Fak Math & Informat, Hagen, Germany

[2] Tech Univ Munich, Zentrum Math, Munich, Germany

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2016年 / 29卷 / 03期

关键词：

Random matrices; Semicircle law; Curie-Weiss model;

D O I：

10.1007/s10959-015-0602-3

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 study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the eigenvalue distribution measure. In case of Curie-Weiss distributions, this criterion applies above the critical temperature (i.e., ). We also investigate the largest eigenvalue of certain ensembles of Curie-Weiss type and find a transition in its behavior at the critical temperature.

引用

页码：1047 / 1068

页数：22

共 23 条

[1]

Anderson Greg W, 2010, INTRO RANDOM MATRICE

[2]

[Anonymous], 1999, Enumerative Combinatorics

[3]

[Anonymous], 1985, Ecole d'Ete de Probabilites de Saint-Flour XIII

[4]

[Anonymous], 1973, Russ. Math. Surv., DOI 10.1070/RM1973v028n01ABEH001396