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arXiv · 2503.12082

Temperleyan Domino Tilings with Holes

Matthew Nicoletti
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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.

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Matthew Nicoletti. 2025-03-15. Temperleyan Domino Tilings with Holes. https://arxiv.org/abs/2503.12082

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