Domino tilings of black-and-white Temperleyan cylinders
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908775250657280 |
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| author | Chelkak, Dmitry Deiman, Zachary |
| author_facet | Chelkak, Dmitry Deiman, Zachary |
| contents | We consider the dimer model in cylindrical domains $Ω_δ$ on square grids of mesh size $δ$ with two Temperleyan boundary components of different colors. Assuming that the $Ω_δ$ approximate a cylindrical domain $Ω$ as $δ\to 0$, we prove the convergence of height fluctuations to the Gaussian Free Field in $Ω$ plus an independent discrete Gaussian multiple of the harmonic measure of one of the boundary components. The limit of the dimer coupling functions on $Ω_δ$ is holomorphic in $Ω$ but not conformally covariant. Given this, we determine the limiting structure of height fluctuations from general principles rather than from explicit computations. In particular, our analysis justifies the inevitable appearance of the discrete Gaussian distribution in the doubly connected setup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Domino tilings of black-and-white Temperleyan cylinders Chelkak, Dmitry Deiman, Zachary Probability Mathematical Physics Complex Variables Primary 82B20, Secondary 30G25, 81T40 We consider the dimer model in cylindrical domains $Ω_δ$ on square grids of mesh size $δ$ with two Temperleyan boundary components of different colors. Assuming that the $Ω_δ$ approximate a cylindrical domain $Ω$ as $δ\to 0$, we prove the convergence of height fluctuations to the Gaussian Free Field in $Ω$ plus an independent discrete Gaussian multiple of the harmonic measure of one of the boundary components. The limit of the dimer coupling functions on $Ω_δ$ is holomorphic in $Ω$ but not conformally covariant. Given this, we determine the limiting structure of height fluctuations from general principles rather than from explicit computations. In particular, our analysis justifies the inevitable appearance of the discrete Gaussian distribution in the doubly connected setup. |
| title | Domino tilings of black-and-white Temperleyan cylinders |
| topic | Probability Mathematical Physics Complex Variables Primary 82B20, Secondary 30G25, 81T40 |
| url | https://arxiv.org/abs/2601.13332 |