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.
