BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Moduli spaces of q-connections and gap probabilities Knizel, Alisa


We will talk about a generalized $q$-analogue of methods introduced by Arinkin and Borodin. In particular we will explain how the one-interval gap probability function for the $q$-Hahn orthogonal polynomial ensemble can be expressed through a solution of the asymmetric $q$-Painlev\'e V equation, which requires a new derivation of a $q$-difference equation of Sakai's hierarchy of type $A_{2}^{(1)}.$ Our approach is based on the analysis of $q$-connections on $\mathbf P^1$ with a particular singularity structure.

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