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تسجيل مستخدم جديدEdge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains
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Jiaoyang Huang
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In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundaries on such domains: with overwhelming probability the tiling height function is within $n^delta$ of its limit shape, and the tiling arctic boundary is within $n^{1/3+delta}$ to its limit shape, for arbitrarily small $delta>0$. This concentration result will be used in [AH21] to prove that the edge statistics of simply-connected polygonal domains, subject to a technical assumption on their limit shape, converge to the Airy line ensemble.
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