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

Abstract

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 planar boundary. The proof does not rely on any exact solvability of the model beyond its links with uniform spanning trees.

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Correspondence to Benoît Laslier.

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Laslier, B. Local limits of lozenge tilings are stable under bounded boundary height perturbations. Probab. Theory Relat. Fields 173, 1243–1264 (2019). https://doi.org/10.1007/s00440-018-0853-x

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Keywords

  • Lozenge tilings
  • Local limit
  • Uniform spanning tree

Mathematics Subject Classification

  • 60K35
  • 82B20