Wenkui Liu: Lozenge tiling with q-class polynomial weights

Abstract

Lozenge tiling in a hexagon with the uniform weights is well studied in the literature. But less is unknown with the general weighs. We studied the random tiling with q-Hahn and complex q-Racah weights, which give the orthonomal polynomial ensembles. And the result (in progress) will show that the push-forward of the scaled height function converges to the Gaussian Free Field with Dirichlet boundary conditions. The method follows by Duits 2018 analysing the limiting behaviours of the recurrence relations of the corresponding orthonomal polynomials.