# $q$-Racah ensemble and $q$-P$\left(E_7^{(1)}/A_{1}^{(1)}\right)$ discrete Painlev\'e equation

@article{Dzhamay2019qRacahEA,
title={\$q\$-Racah ensemble and \$q\$-P\$\left(E\_7^\{(1)\}/A\_\{1\}^\{(1)\}\right)\$ discrete Painlev\'e equation},
author={Anton Dzhamay and Alisa Knizel},
journal={arXiv: Mathematical Physics},
year={2019}
}
• Published 14 March 2019
• Mathematics
• arXiv: Mathematical Physics
The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painleve equations. Namely, we consider the $q$-Racah polynomial ensemble and show that the one-interval gap probabilities in this case can be expressed through a solution of the discrete $q$-P$\left(E_7^{(1)}/A_{1}^{(1)}\right)$ equation. Our approach also gives a new Lax pair for this equation. This Lax pair has an interesting additional involutive…
1 Citations

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