Temperleyan Domino Tilings with Holes
Abstract
We analyze asymptotic height function fluctuations in uniformly random domino tiling models on multiply connected Temperleyan domains. Starting from asymptotic formulas derived by Kenyon [arXiv:math-ph/9910002v1], we show that (1) the difference of the centered height function and a harmonic function with boundary values given by the (random) centered hole heights converges in the sense of moments to a Gaussian free field, which is independent of the hole heights, and (2) the hole heights themselves converge in distribution to a discrete Gaussian random vector. These results confirm general predictions about height fluctuations for tilings on multiply connected domains.
Keywords
Cite
@article{arxiv.2503.12082,
title = {Temperleyan Domino Tilings with Holes},
author = {Matthew Nicoletti},
journal= {arXiv preprint arXiv:2503.12082},
year = {2025}
}
Comments
v2: 18 pages, 2 figures. Modified Sec 1.1, added references and further discussion of related work