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
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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.
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页码：202 / 224
页数：22
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