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Discrete gap probabilities and discrete Painlevé equations (2003)
| Venue: | DUKE MATH J |
| Citations: | 29 - 6 self |
BibTeX
@ARTICLE{Borodin03discretegap,
author = {Alexei Borodin},
title = {Discrete gap probabilities and discrete Painlevé equations},
journal = { DUKE MATH J},
year = {2003},
volume = {117},
number = {3},
pages = {209144}
}
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Abstract
We prove that Fredholm determinants of the form det(1 − Ks), where Ks is the restriction of either the discrete Bessel kernel or the discrete 2F1-kernel to {s, s + 1,...}, can be expressed, respectively, through solutions of discrete Painlevé II (dPII) and Painlevé V (dPV) equations. 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 eη(ζ +ζ −1) and (1 + ξζ)
