Edge Universality of Beta Ensembles

被引：89

作者：

Bourgade, Paul ^{[1
]}

Erdoes, Laszlo ^{[2
]}

Yau, Horng-Tzer ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] IST Austria, A-3400 Klosterneuburg, Austria

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2014年 / 332卷 / 01期

基金：

美国国家科学基金会;

关键词：

GENERALIZED WIGNER MATRICES; LOCAL EIGENVALUE STATISTICS; DENSITY-OF-STATES; BULK UNIVERSALITY; ORTHOGONAL POLYNOMIALS; EXPONENTIAL WEIGHTS; HERMITIAN MATRICES; LARGE DEVIATIONS; MODELS; UNITARY;

D O I：

10.1007/s00220-014-2120-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove the edge universality of the beta ensembles for any , provided that the limiting spectrum is supported on a single interval, and the external potential is and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class l(4).

引用

页码：261 / 353

页数：93

共 62 条

[1] On the 1/n expansion for some unitary invariant ensembles of random matrices [J].