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

TL;DR

This paper proves that small boundary modifications in lozenge tilings do not alter local configurations, establishing the stability of local limits across various domains with planar boundaries.

Contribution

It demonstrates the stability of local limits of lozenge tilings under bounded boundary height perturbations, independent of exact solvability.

Findings

Local behavior remains unchanged under boundary perturbations.

Existence of local limits in all planar boundary domains.

Proof relies on connections with uniform spanning trees.

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.