Universal behavior for averages of characteristic polynomials at the origin of the spectrum
| dc.creator | Vanlessen, M. | |
| dc.date | 2003-06-30 | |
| dc.date.accessioned | 2026-07-07T04:30:20Z | |
| dc.date.available | 2026-07-07T04:30:20Z | |
| dc.description | It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy transforms. We will show that, for the unitary ensemble $\frac{1}{\hat Z_n}|\det M|^{2α}e^{-nV(M)}dM$ of $n\times n$ Hermitian matrices, these kernels have universal behavior at the origin of the spectrum, as $n\to\infty$, in terms of Bessel functions. Our approach is based on the characterization of orthogonal polynomials together with their Cauchy transforms via a matrix Riemann-Hilbert problem, due to Fokas, Its and Kitaev, and on an application of the Deift/Zhou steepest descent method for matrix Riemann-Hilbert problems to obtain the asymptotic behavior of the Riemann-Hilbert problem. | |
| dc.description | 24 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0306078 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0306078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57434 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Universal behavior for averages of characteristic polynomials at the origin of the spectrum | |
| dc.type | text |