• Corpus ID: 237352940

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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References

SHOWING 1-10 OF 50 REFERENCES

Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains

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

Tilings of Non-convex Polygons, Skew-Young Tableaux and Determinantal Processes

This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new

Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field

We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows

Probability distributions related to tilings of non-convex polygons

This paper is based on the study of random lozenge tilings of non-convex polygonal regions with interacting non-convexities (cuts) and the corresponding asymptotic kernel as in [3] and [4] (discrete

Lozenge Tilings of Hexagons with Cuts and Asymptotic Fluctuations: a New Universality Class

This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposite cuts in the

Local statistics for random domino tilings of the Aztec diamond

We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will

Non-intersecting paths, random tilings and random matrices

Abstract. We investigate certain measures induced by families of non-intersecting paths in domino tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a cylindrical brick

Bulk Universality for Random Lozenge Tilings Near Straight Boundaries and for Tensor Products

We prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains. The result applies to uniformly

Local limits of lozenge tilings are stable under bounded boundary height perturbations

  • B. Laslier
  • Mathematics
    Probability Theory and Related Fields
  • 2018
We show that bounded changes to the boundary of a lozenge tilings do not affect the local behaviour inside the domain. As a consequence we prove the existence of a local limit in all domains with

Universal edge fluctuations of discrete interlaced particle systems

We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently