A phase transition for the limiting spectral density of random matrices

被引：14

作者：

Friesen, Olga ^{[1
]}

Loewe, Matthias ^{[1
]}

机构：

[1] Univ Munster, Munster, Germany

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2013年 / 18卷

关键词：

random matrices; dependent random variables; Toeplitz matrices; semicircle law; Curie-Weiss model; SEMICIRCLE LAW;

D O I：

10.1214/EJP.v18-2118

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 analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation, the limiting spectral distribution is either the famous semicircle distribution, the distribution derived for Toeplitz matrices by Bryc, Dembo and Jiang (2006), or the free convolution of the two distributions.

引用

页码：1 / 17

页数：17

共 20 条

[1]

[Anonymous], 1978, MATH PROBLEMS THEORE

[2]

[Anonymous], 2006, LECT COMBINATORICS F, DOI DOI 10.1017/CBO9780511735127

[3] WIGNERS SEMICIRCLE LAW FOR EIGENVALUES OF RANDOM MATRICES [J].