Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble
| dc.creator | Bianchi, P. | |
| dc.creator | Debbah, M. | |
| dc.creator | Najim, J. | |
| dc.date | 2008-11-06 | |
| dc.date.accessioned | 2026-07-07T10:16:26Z | |
| dc.date.available | 2026-07-07T10:16:26Z | |
| dc.description | Consider a $n \times n$ matrix from the Gaussian Unitary Ensemble (GUE). Given a finite collection of bounded disjoint real Borel sets $(Δ_{i,n},\ 1\leq i\leq p)$, properly rescaled, and eventually included in any neighbourhood of the support of Wigner's semi-circle law, we prove that the related counting measures $({\mathcal N}_n(Δ_{i,n}), 1\leq i\leq p)$, where ${\mathcal N}_n(Δ)$ represents the number of eigenvalues within $Δ$, are asymptotically independent as the size $n$ goes to infinity, $p$ being fixed. As a consequence, we prove that the largest and smallest eigenvalues, properly centered and rescaled, are asymptotically independent; we finally describe the fluctuations of the condition number of a matrix from the GUE. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0811.0979 | |
| dc.identifier | http://arxiv.org/abs/0811.0979 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173504 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 15A52 | |
| dc.title | Asymptotic Independence in the Spectrum of the Gaussian Unitary Ensemble | |
| dc.type | text |