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. https://resolver.caltech.edu/CaltechAUTHORS:20171106-141427328
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Abstract
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.
Item Type: | Article | ||||||||||||
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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 | ||||||||||||
DOI: | 10.1007/s00440-002-0250-2 | ||||||||||||
Record Number: | CaltechAUTHORS:20171106-141427328 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171106-141427328 | ||||||||||||
Official Citation: | Rains, E. Probab. Theory Relat. Fields (2003) 125: 522. https://doi.org/10.1007/s00440-002-0250-2 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 82994 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 06 Nov 2017 23:16 | ||||||||||||
Last Modified: | 15 Nov 2021 19:54 |
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