Over the last decade it became clear that discrete Painlevéequations appear in a wide range of interesting applications. Thus, the question is to recognize a certain nonautonomous recurrence as a discrete Painlevé equation andunderstanding its position in Sakai’s classification scheme,Fortunately, Sakai’s geometric theory provides an almost algorithmic procedureof answering this question. In this talk we illustrate this procedure by considering the problem of tiling a hexagon by lozenges with some generalized weight and we are interested in computing important statistical propertiesof this model called the gap probabilities. This model can be related to a qRacah discrete orthogonal polynomial ensemble, and this computation is again done with the help of discrete Painlevé equation. This is a joint work with Alisa Knizel (Columbia University).
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Discrete Painlevé Equations and Orthogonal Polynomials and tiling
Research Group:
Speaker:
Anton Dzhamay
Institution:
University of Northern Colorado
Schedule:
Monday, June 12, 2023  12:00
Location:
A135
Abstract:
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