Permutation Matrices, Wreath Products, and the Distribution of Eigenvalues

Kelly Wieand ()
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Kelly Wieand: University of Chicago

Journal of Theoretical Probability, 2003, vol. 16, issue 3, 599-623

Abstract: Abstract We consider a class of random matrix ensembles which can be constructed from the random permutation matrices by replacing the nonzero entries of the n×n permutation matrix matrix with M×M diagonal matrices whose entries are random Kth roots of unity or random points on the unit circle. Let X be the number of eigenvalues lying in a specified arc I of the unit circle, and consider the standardized random variable (X−E[X])/(Var(X))1/2. We show that for a fixed set of arcs I 1,...,I N , the corresponding standardized random variables are jointly normal in the large n limit, and compare the covariance structures which arise with results for other random matrix ensembles.

Keywords: random matrices; permutations; wreath products (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1025616431496

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