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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.26664 |
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| _version_ | 1866916047342272512 |
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| author | Aggarwal, Amol Toninelli, Fabio |
| author_facet | Aggarwal, Amol Toninelli, Fabio |
| contents | We prove that the continuous-time, single-flip Glauber dynamics for lozenge tilings of the size-$N$ hexagon mix in time $N^{2+o(1)}$. This was predicted to hold on fairly general domains of diameter $N$ (on the basis of the ``Lifshitz law'' heuristic) but had previously only been established in domains such that the associated limit shape has no frozen facets. To access the hexagon, we introduce a multi-scale comparison argument between the height function of the random tiling evolving under the Glauber dynamics and the limit shape of a volume-tilted tiling (whose tilting parameter varies suitably in time). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mixing times for Glauber dynamics of lozenge tilings of the hexagon Aggarwal, Amol Toninelli, Fabio Probability We prove that the continuous-time, single-flip Glauber dynamics for lozenge tilings of the size-$N$ hexagon mix in time $N^{2+o(1)}$. This was predicted to hold on fairly general domains of diameter $N$ (on the basis of the ``Lifshitz law'' heuristic) but had previously only been established in domains such that the associated limit shape has no frozen facets. To access the hexagon, we introduce a multi-scale comparison argument between the height function of the random tiling evolving under the Glauber dynamics and the limit shape of a volume-tilted tiling (whose tilting parameter varies suitably in time). |
| title | Mixing times for Glauber dynamics of lozenge tilings of the hexagon |
| topic | Probability |
| url | https://arxiv.org/abs/2605.26664 |