Lozenge Tilings of Hexagons with Cuts and Asymptotic Fluctuations: a New Universality Class

Abstract

This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposite cuts in the regions, when the size of the regions tend to infinity, together with the cuts. It leads to a new kernel, which is expected to have universality properties.