A Fredholm determinant formula for Toeplitz determinants
| dc.creator | Borodin, Alexei | |
| dc.creator | Okounkov, Andrei | |
| dc.date | 1999-07-25 | |
| dc.date.accessioned | 2026-07-07T05:30:04Z | |
| dc.date.available | 2026-07-07T05:30:04Z | |
| dc.description | We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1-K acting on l_2({n,n+1,...}), where the kernel K admits an integral representation in terms of the symbol of the original Toeplitz matrix. The proof is based on the results of one of the authors, see math.RT/9907127, and a formula due to Gessel which expands any Toeplitz determinant into a series of Schur functions. We also consider 3 examples where the kernel involves the Gauss hypergeometric function and its degenerations. | |
| dc.identifier | https://arxiv.org/abs/math/9907165 | |
| dc.identifier | http://arxiv.org/abs/math/9907165 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78876 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Representation Theory | |
| dc.title | A Fredholm determinant formula for Toeplitz determinants | |
| dc.type | text |