Comportement asymptotique des polynômes orthogonaux associés à un poids ayant un zéro d'ordre fractionnaire sur le cercle. Applications aux valeurs propres d'une classe de matrices aléatoires unitaires
| dc.creator | Rambour, Philippe | |
| dc.creator | Seghier, Abdellatif | |
| dc.date | 2009-04-05 | |
| dc.date | 2009-04-27 | |
| dc.date.accessioned | 2026-07-07T13:08:21Z | |
| dc.date.available | 2026-07-07T13:08:21Z | |
| dc.description | Asymptotic behavior of orthogonal polynomials on the circle, with respect to a weight having a fractional zero on the torus. Applications to the eigenvalues of certain unitary random matrices. This paper is devoted to the orthogonal polynomial on the circle, with respect to a weight of type $ f=(1-\cos θ)^αc$ where $c$ is a sufficiently smooth function and $α\in ]-{1/2}, {1/2}[$. We obtain an asymptotic expansion of the coefficients of this polynomial and of $Φ^{(p)}_{N}(1)$ for all integer $p$. These results allow us to obtain an asymptotic expansion of the associated Christofel-Darboux kernel, and to compute the distribution of the eigenvalues of a family of random unitary matrices. The proof of the resuts related with the orthogonal polynomials are essentialy based on the inversion of Toeplitz matice associated to the symbol $f$. | |
| dc.identifier | https://arxiv.org/abs/0904.0777 | |
| dc.identifier | http://arxiv.org/abs/0904.0777 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228391 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 47B39; 47BXX | |
| dc.title | Comportement asymptotique des polynômes orthogonaux associés à un poids ayant un zéro d'ordre fractionnaire sur le cercle. Applications aux valeurs propres d'une classe de matrices aléatoires unitaires | |
| dc.type | text |