Asymptotics of random domino tilings of rectangular Aztec diamonds

Alexey Bufetov; Alisa Knizel

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arXiv · 1604.01491

Asymptotics of random domino tilings of rectangular Aztec diamonds

Alexey Bufetov·Alisa Knizel

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Abstract

We consider asymtotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a special class of examples, the explicit parametrization of the frozen boundary is given. It turns out to be an algebraic curve with very special properties. Moreover, we establish the convergence of the fluctuations to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems.

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BibTeX RIS

Alexey Bufetov, Alisa Knizel. 2016-04-06. Asymptotics of random domino tilings of rectangular Aztec diamonds. https://arxiv.org/abs/1604.01491

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