Open Access
October 2000 Eigenvalue distributions of random permutation matrices
Kelly Wieand
Ann. Probab. 28(4): 1563-1587 (October 2000). DOI: 10.1214/aop/1019160498


Let $M$ be a randomly chosen $n \times n$ permutation matrix. For a fixed arc of the unit circle, let $X$ be the number of eigenvalues of $M$ which lie in the specified arc. We calculate the large $n$ asymptotics for the mean and variance of $X$, and show that $(X -E[X])/( \text{Var} (X))^ {1/2}$ is asymptotically normally distributed. In addition, we show that for several fixed arcs $I_1,\ldots,I_m$, the corresponding random variables are jointly normal in the large $n$ limit.


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Kelly Wieand. "Eigenvalue distributions of random permutation matrices." Ann. Probab. 28 (4) 1563 - 1587, October 2000.


Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.15017
MathSciNet: MR1813834
Digital Object Identifier: 10.1214/aop/1019160498

Primary: 15A52 , 60B15
Secondary: 60C05 , 60F05

Keywords: permutations , random matrices

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 4 • October 2000
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