Universality at the edge of the spectrum in Wigner random matrices

被引：237

作者：

Soshnikov, A ^{[1
]}

机构：

[1] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1999年 / 207卷 / 03期

关键词：

D O I：

10.1007/s002200050743

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove universality at the edge for rescaled correlation functions of Wigner random matrices in the limit n --> +infinity. As a corollary, we show that, after proper rescaling, the 1(th), 2(nd), 3(rd), etc. eigenvalues of Wigner random hermitian (resp. real symmetric) matrix weakly converge to the distributions established by Tracy and Widom in G.U.E. (G.O.E.) cases.

引用

页码：697 / 733

页数：37

共 54 条

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