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Inhomogeneous Tilings of the Aztec Diamond

Student-Run Applied & Math Seminar

Speaker: Gregory Shinault, GGAM
Location: 2112 MSB
Start time: Wed, Apr 11 2012, 12:10PM

Random domino tilings of the Aztec diamond have been a subject of much interest in the past 20 years. The main result of the subject, the Arctic Circle theorem, is a gem of modern mathematics which gives the limiting shape of the tiling. When we examine fluctuations around the limiting shape, we do not see a Gaussian distribution as one might expect in classical probability. Instead we see the Tracy-Widom GUE distribution of random matrix theory. These theorems were originally proven for a random tiling chosen by a uniform distribution. In this talk we examine the effects of choosing the tiling via a distribution in an inhomogeneous environment (and we'll explain what we mean by this!).