Discrete gap probabilities and discrete Painleve equations
| dc.creator | Borodin, Alexei | |
| dc.date | 2001-11-05 | |
| dc.date.accessioned | 2026-07-07T04:28:44Z | |
| dc.date.available | 2026-07-07T04:28:44Z | |
| dc.description | We prove that Fredholm determinants of the form det(1-K_s), where K_s is the restriction of either the discrete Bessel kernel or the discrete {}_2F_1 kernel to {s,s+1,...}, can be expressed through solutions of discrete Painleve II and V equations, respectively. These Fredholm determinants can also be viewed as distribution functions of the first part of the random partitions distributed according to a poissonized Plancherel measure and a z-measure, or as normalized Toeplitz determinants with symbols exp(η(u+1/u)) and (1+u)^z(1+ξ/u)^{z'}. The proofs are based on a general formalism involving discrete integrable operators and discrete Riemann-Hilbert problem. A continuous version of the formalism has been worked out in math-ph/0111007. | |
| dc.description | AMSTeX, 43 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math-ph/0111008 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0111008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56901 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Discrete gap probabilities and discrete Painleve equations | |
| dc.type | text |