Distribution of the first particle in discrete orthogonal polynomial ensembles

Borodin, Alexei; Boyarchenko, Dmitriy

doi:10.1007/s00220-002-0767-3

arXiv 2002-04-01 DOI 10.1007/s00220-002-0767-3 0 views

Distribution of the first particle in discrete orthogonal polynomial ensembles

Borodin, Alexei · Boyarchenko, Dmitriy

Mathematical Physics Condensed Matter High Energy Physics - Theory Classical Analysis and ODEs Exactly Solvable and Integrable Systems

Original · EN

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.

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