Random sampling of domino and lozenge tilings

Abstract

A grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different strategies to generate random tilings of large grid regions in the plane. This makes it possible to observe the behaviour of large random tilings, in particular the occurrence of boundary phenomena that have been the subject of intensive recent research.