# Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble

@inproceedings{Aggarwal2021EdgeSF, title={Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble}, author={Amol Aggarwal and Jiaoyang Huang}, year={2021} }

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…

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