Eigenvalue distributions of random permutation matrices
成果类型：
Article
署名作者：
Wieand, K
署名单位：
University of Arizona
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1019160498
发表日期：
2000
页码：
1563-1587
关键词：
摘要：
Let M be a randomly chosen n x n permutation matrix. For a fixed are of the unit circle, let X be the number of eigenvalues of M which lie in the specified are. We calculate the large n asymptotics for the mean and variance of X, and show that (X - E[X])/(Var(X))(1/2) is asymptotically normally distributed. In addition, we show that for several fixed arcs I-1,...,I-m, the corresponding random variables are jointly normal in the large n limit.