A variational principle for domino tilings of multiply-connected domains
arXiv:2110.06896
Abstract
We study random domino tilings of a multiply-connected domain with a height function defined on the universal covering space of the domain. We prove a large deviation principle for the height function in two asymptotic regimes. The first regime covers all domino tilings of the domain. We also prove a law of large numbers for height change in this regime. The second regime covers domino tilings with a given asymptotic height change .
32 pages, 14 figures, rewritten structure of the paper and introduction, some changes in notations