Workshop: Fock’s dimer model on the Aztec diamond

Speaker
Béatrice de Tilière, University Paris-Dauphine PSL

Abstract
We consider the dimer model, or equivalently domino tilings, on the Aztec diamond, and suppose that edges are assigned Fock’s weights. The main goal of this talk is to give a compact, explicit formula for the inverse Kasteleyn matrix, thus extending in this very general context previous results of the same kind; in particular, this gives an explicit expression for Boltzmann probabilities. Then, we will prove that the partition function admits a product form, and show how to recover Stanley’s celebrated formula as a specific case. Finally, we will show how our expression for the inverse Kasteleyn matrix allows to recover results about limit shapes. This is based on joint work with Cédric Boutillier (Sorbonne University).