Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle
| dc.creator | Krasovsky, I. V. | |
| dc.date | 2004-01-20 | |
| dc.date | 2004-04-22 | |
| dc.date.accessioned | 2026-07-07T05:04:42Z | |
| dc.date.available | 2026-07-07T05:04:42Z | |
| dc.description | We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant with the kernel $\sin z/(πz)$ on the interval $[0,s]$, verifying a conjecture of Dyson for the constant term in the expansion. In the Gaussian Unitary Ensemble of random matrices, this determinant describes the probability for an interval of length $s$ in the bulk scaling limit to be free from the eigenvalues. | |
| dc.description | 20 pages, 1 figure, small changes | |
| dc.identifier | https://arxiv.org/abs/math/0401258 | |
| dc.identifier | http://arxiv.org/abs/math/0401258 | |
| dc.identifier | Int.Math.Res.Not. 2004 (2004), no.25, 1249-1272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69906 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.title | Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle | |
| dc.type | text |