• Corpus ID: 237352940

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

  title={Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble},
  author={Amol Aggarwal and Jiaoyang Huang},
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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  • B. Laslier
  • Mathematics
    Probability Theory and Related Fields
  • 2018
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