Tomas Berggren: Domino tilings of the Aztec diamond with doubly periodic weightings

Abstract

This talk will be centered around random domino tilings of the Aztec diamond with doubly periodic weightings. In particular asymptotic results of the \(2\times k\)-periodic Aztec diamond will be discussed, both in the macroscopic and microscopic scale. The macroscopic picture is described using a close connection to a Riemann surface. For instance, the number of smooth regions (also called gas regions) is the same as the genus of the mentioned Riemann surface.