Temperleyan Domino Tilings with Holes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915259457994752 |
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| author | Nicoletti, Matthew |
| author_facet | Nicoletti, Matthew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Temperleyan Domino Tilings with Holes Nicoletti, Matthew Probability Mathematical Physics Complex Variables 82B20 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. |
| title | Temperleyan Domino Tilings with Holes |
| topic | Probability Mathematical Physics Complex Variables 82B20 |
| url | https://arxiv.org/abs/2503.12082 |