Mathematics

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 non-autonomous 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 q-Racah 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).