Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble ...
We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency location, converge to the Airy line ensemble. Our proof proceeds...
| Main Authors: | , |
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| Format: | Report |
| Language: | unknown |
| Published: |
arXiv
2021
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2108.12874 https://arxiv.org/abs/2108.12874 |
| Summary: | We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency location, converge to the Airy line ensemble. Our proof proceeds by locally comparing these edge statistics with those for a random tiling of a hexagon, which are well understood. To realize this comparison, we require a nearly optimal concentration estimate for the tiling height function, which we establish by exhibiting a certain Markov chain on the set of all tilings that preserves such concentration estimates under its dynamics. ... : 57 pages, 12 figures; Version 2: Minor edits ... |
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