Distribution of the first particle in discrete orthogonal polynomial ensembles
Mathematical Physics
2009-11-07 v1 Condensed Matter
High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
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.
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Cite
@article{arxiv.math-ph/0204001,
title = {Distribution of the first particle in discrete orthogonal polynomial ensembles},
author = {Alexei Borodin and Dmitriy Boyarchenko},
journal= {arXiv preprint arXiv:math-ph/0204001},
year = {2009}
}
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41 pages