$q$-Racah ensemble and $q$-P$\left(E_7^{(1)}/A_1^{(1)}\right)$ discrete Painlevé equation

Anton Dzhamay, Alisa Knizel

The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlevé equations. Namely, we conside…