Eigenvalue distributions of random unitary matrices

被引：0

作者：

K. Wieand

机构：

[1] Department of Health Studies,

[2] University of Chicago,undefined

[3] 5841 S. Maryland Ave.,undefined

[4] MC 2007,undefined

[5] Chicago,undefined

[6] IL 60637,undefined

[7] USA. e-mail: klwieand@post.harvard.edu,undefined

来源：

Probability Theory and Related Fields | 2002年 / 123卷

关键词：

Unit Circle; Random Matrix; Unitary Group; Unitary Matrice; Eigenvalue Distribution;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let U be an n × n random matrix chosen from Haar measure on the unitary group. For a fixed arc of the unit circle, let X be the number of eigenvalues of M which lie in the specified arc. We study this random variable as the dimension n grows, using the connection between Toeplitz matrices and random unitary matrices, and show that (X -E [X])/(\Var (X))1/2 is asymptotically normally distributed. In addition, we show that for several fixed arcs I1, ..., Im, the corresponding random variables are jointly normal in the large n limit.

引用

页码：202 / 224

页数：22