The birth of a cut in unitary random matrix ensembles
| dc.creator | Claeys, Tom | |
| dc.date | 2007-11-16 | |
| dc.date.accessioned | 2026-07-07T08:43:23Z | |
| dc.date.available | 2026-07-07T08:43:23Z | |
| dc.description | We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a bounded number of eigenvalues is expected in the newborn cut. It turns out that limits of the eigenvalue correlation kernel are given by Hermite kernels corresponding to a finite size Gaussian Unitary Ensemble (GUE). When modifying the double scaling limit slightly, we observe a remarkable transition each time the new cut picks up an additional eigenvalue, leading to a limiting kernel interpolating between GUE-kernels for matrices of size k and size k+1. We prove our results using the Riemann-Hilbert approach. | |
| dc.description | 28 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0711.2609 | |
| dc.identifier | http://arxiv.org/abs/0711.2609 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142298 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Complex Variables | |
| dc.subject | 15A52; 35Q15; 33C45 | |
| dc.title | The birth of a cut in unitary random matrix ensembles | |
| dc.type | text |