Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices
| dc.creator | Petz, Denes | |
| dc.creator | Reffy, Julia | |
| dc.date | 2004-09-28 | |
| dc.date | 2004-10-01 | |
| dc.date.accessioned | 2026-07-07T05:12:40Z | |
| dc.date.available | 2026-07-07T05:12:40Z | |
| dc.description | Let $U_m$ be an $m \times m$ Haar unitary matrix and $U_{[m,n]}$ be its $n \times n$ truncation. In this paper the large deviation is proven for the empirical eigenvalue density of $U_{[m,n]}$ as $m/n \to λ$ and $n \to \infty$. The rate function and the limit distribution are given explicitly. $U_{[m,n]}$ is the random matrix model of $quq$, where $u$ is a Haar unitary in a finite von Neumann algebra, $q$ is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator $quq$. | |
| dc.identifier | https://arxiv.org/abs/math/0409552 | |
| dc.identifier | http://arxiv.org/abs/math/0409552 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72659 | |
| dc.subject | Probability | |
| dc.subject | 60F10; 15A52 | |
| dc.title | Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices | |
| dc.type | text |