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Probability Theory and Related Fields

, Volume 173, Issue 3–4, pp 1243–1264 | Cite as

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

  • Benoît LaslierEmail author
Article
  • 43 Downloads

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.

Keywords

Lozenge tilings Local limit Uniform spanning tree 

Mathematics Subject Classification

60K35 82B20 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Paris DiderotParisFrance

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