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• W2951786801 abstract "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(eta(u+1/u)) and (1+u)^z(1+xi/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." @default.
• W2951786801 created "2019-06-27" @default.
• W2951786801 creator A5059587630 @default.
• W2951786801 date "2001-11-05" @default.
• W2951786801 modified "2023-09-27" @default.
• W2951786801 title "Discrete gap probabilities and discrete Painleve equations" @default.
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• W2951786801 hasPublicationYear "2001" @default.
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