Dimer models on astroidal zig-zag graphs

The dimer model refers to the study of random dimer covers (or perfect matchings) of a bipartite graph. A remarkable feature of these models is the emergence of limit shapes: in large periodic graphs, a random matching concentrates around a deterministic shape. Although general dimer models exhibit limit shapes, they are well understood only in some classical cases like the hexagonal and square lattices, corresponding to lozenge and domino tilings. In this talk, I will explain how ideas coming from integrable systems make it possible to study limit shapes for general dimer models.

This is based on joint work in progress with Tomas Berggren and Alexei Borodin.