Images of eigenvalue distributions under power maps
| dc.creator | Rains, Eric M. | |
| dc.date | 2000-08-10 | |
| dc.date.accessioned | 2026-07-07T04:36:44Z | |
| dc.date.available | 2026-07-07T04:36:44Z | |
| dc.description | In [earlier work by the author], it was shown that if U is a random n x 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. | |
| dc.description | 15 pages, LaTeX (multicol, AMS macros) | |
| dc.identifier | https://arxiv.org/abs/math/0008079 | |
| dc.identifier | http://arxiv.org/abs/math/0008079 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59708 | |
| dc.subject | Probability | |
| dc.subject | Representation Theory | |
| dc.subject | 15A52 (22E99 60B15) | |
| dc.title | Images of eigenvalue distributions under power maps | |
| dc.type | text |