Distribution of the first particle in discrete orthogonal polynomial ensembles

Abstract

We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational. In a number of classical special cases the recurrence procedure is equivalent to the difference and q-Painleve equations of chao-dyn/9507010, [Sakai]. Our approach is based on the formalism of discrete integrable operators and discrete Riemann--Hilbert problems developed in math.CO/9912093, math-ph/0111008.

41 pages

References in corpus (3)

• Riemann-Hilbert problems for last passage percolation
• Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory
• Recursion relations for Unitary integrals, Combinatorics and the Toeplitz Lattice

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