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

Autor:	Dzhamay, Anton, Knizel, Alisa
Rok vydání:	2019
Předmět:	Mathematical Physics Mathematics - Algebraic Geometry Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlev\'e 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 symmetry structure.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.06159 Zobrazit plný text záznamu View this record from Arxiv