Deformed ensembles of random matrices

被引：0

作者：

Peche, Sandrine ^{[1
]}

机构：

[1] Univ Paris Diderot, 5 Rue Thomas Mann, F-75013 Paris, France

来源：

PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL III | 2014年

关键词：

Probability; random matrices; separation of eigenvalues; universality; CENTRAL LIMIT-THEOREMS; LARGEST EIGENVALUE; FREE CONVOLUTION; UNIVERSALITY; DEFORMATIONS; FLUCTUATIONS; CONVERGENCE; PERCOLATION; STATISTICS; LAW;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we review recent results in the study of asymptotic spectral properties of some perturbation of large random matrices. Deformed models have arisen in random matrix theory in Baik, J.; Ben Arous, G.; Peche S. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 (2005), no. 5, 1643-1697. In this review, we consider additive or multiplicative deformations of standard Wigner or sample covariance matrices. We consider the phenomenon of separation of extreme eigenvalues and the question of universality of their asymptotic distribution for random matrices with a non necessarily Gaussian distribution.

引用

页码：1159 / 1174

页数：16