​Christophe Charlier: Doubly periodic lozenge tilings of a hexagon and matrix valued orthogonal polynomials

Abstract

I will present some results on a random lozenge tiling model of a large regular hexagon, whose underlying weight structure is periodic of period 2 in both the horizontal and vertical directions. This is a determinantal point process whose correlation kernel is expressed in terms of non-Hermitian matrix valued orthogonal polynomials. I will also discuss the techniques used in the proof. The starting point is a double contour formula (obtained by Duits and Kuijlaars) which involves the solution of a 4x4 Riemann-Hilbert problem.