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On the eigenvalues of random matrices

Published online by Cambridge University Press:  05 September 2017

Persi Diaconis  and
Mehrdad Shahshahani
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Abstract

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Let M be a random matrix chosen from Haar measure on the unitary group Un. Let Z = X + iY be a standard complex normal random variable with X and Y independent, mean 0 and variance ½ normal variables. We show that for j = 1, 2, …, Tr(Mj) are independent and distributed as √jZ asymptotically as n →∞. This result is used to study the set of eigenvalues of M. Similar results are given for the orthogonal and symplectic and symmetric groups.

Keywords

HAAR MEASUREORTHOGONAL GROUPSSYMPLECTIC GROUPSSYMMETRIC GROUPS
Type
Part 2 Probabilistic Methods
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 49 - 62
Copyright
Copyright © Applied Probability Trust 1994 

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