Abstract: This talk will be centered around domino tilings, or dimer coverings, of the Aztec diamond with doubly periodic edge weights. Such model exhibits a rich structure, for instance, in the limit three types of regions may appear, the frozen, rough and smooth regions (also known as solid, liquid and gas regions). We will discuss asymptotic results, both on the macroscopic and microscopic scale.

The asymptotic results rely on an expression of the correlation kernel in terms of a Wiener-Hopf factorization of a matrix valued function, which is defined in terms of the edge weights. If time permits, we will discuss how such Wiener-Hopf factorization sometimes can be obtained in a form that are suitable for asymptotic analysis.