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Images of eigenvalue distributions under power maps

Rains, Eric M. (2003) Images of eigenvalue distributions under power maps. Probability Theory and Related Fields, 125 (4). pp. 522-538. ISSN 0178-8051. doi:10.1007/s00440-002-0250-2.

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In [9], it was shown that if U is a random n×n unitary matrix, then for any p≥n, the eigenvalues of U^p are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens when p<n instead. For the classical groups, we find that we can describe the eigenvalue distribution of U^p in terms of the eigenvalue distributions of smaller classical groups; the earlier result is then a special case. The proofs rely on the fact that a certain subgroup of the Weyl group is itself a Weyl group. We generalize this fact, and use it to study the power-map problem for general compact Lie groups.

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Additional Information:© 2003 Springer-Verlag Berlin Heidelberg. Received: 19 December 2000; Revised version: 7 August 2002; Published online: 21 February 2003.
Issue or Number:4
Record Number:CaltechAUTHORS:20171106-141427328
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Official Citation:Rains, E. Probab. Theory Relat. Fields (2003) 125: 522.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82994
Deposited By: Tony Diaz
Deposited On:06 Nov 2017 23:16
Last Modified:15 Nov 2021 19:54

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