学术报告（Arno Kuijlaars 2025.4.10）

Abstract: Large random tilings of a hexagon have the fascinating behavior of distinct asymptotic phases (frozen and rough; also called solid and liquid) separated by a well-defined Arctic curve. In a weighted tiling model with periodically varying weights a third phase (smooth; or gaseous) appears where correlations between tiles decay at an exponential rate.
After a general introduction, I will discuss an approach towards a rigorous analysis of a three periodic hexagon tiling model, that includes matrix valued orthogonal polynomials, Riemann-Hilbert problems, and steepest descent analysis on a Harnack curve.