A variational principle for domino tilings of multiply-connected domains
Probability
2023-08-29 v4 Mathematical Physics
Combinatorics
math.MP
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 .
Keywords
Cite
@article{arxiv.2110.06896,
title = {A variational principle for domino tilings of multiply-connected domains},
author = {Nikolai Kuchumov},
journal= {arXiv preprint arXiv:2110.06896},
year = {2023}
}
Comments
32 pages, 14 figures, rewritten structure of the paper and introduction, some changes in notations