Asymptotics of random domino tilings of rectangular Aztec diamonds
Probability
2017-06-23 v3 Mathematical Physics
Combinatorics
math.MP
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.
Keywords
Cite
@article{arxiv.1604.01491,
title = {Asymptotics of random domino tilings of rectangular Aztec diamonds},
author = {Alexey Bufetov and Alisa Knizel},
journal= {arXiv preprint arXiv:1604.01491},
year = {2017}
}