Powers of large random unitary matrices and Toeplitz determinants
| dc.creator | Duits, Maurice | |
| dc.creator | Johansson, Kurt | |
| dc.date | 2006-07-11 | |
| dc.date | 2007-04-24 | |
| dc.date.accessioned | 2026-07-07T07:57:53Z | |
| dc.date.available | 2026-07-07T07:57:53Z | |
| dc.description | We study the limiting behavior of $\Tr U^{k(n)}$, where $U$ is a $n\times n$ random unitary matrix and $k(n)$ is a natural number that may vary with $n$ in an arbitrary way. Our analysis is based on the connection with Toeplitz determinants. The central observation of this paper is a strong Szegö limit theorem for Toeplitz determinants associated to symbols depending on $n$ in a particular way. As a consequence to this result, we find that for each fixed $m\in \N$, the random variables $ \Tr U^{k_j(n)}/\sqrt{\min(k_j(n),n)}$, $j=1,..., m$, converge to independent standard complex normals. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0607017 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0607017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127812 | |
| dc.subject | Mathematical Physics | |
| dc.title | Powers of large random unitary matrices and Toeplitz determinants | |
| dc.type | text |