Does a portion of dimer configuration determines its domain of definition?

TL;DR

This paper proves that in the wired uniform spanning tree and temperleyan dimer model, boundary condition changes do not have a singular effect on the model's measure away from the boundary, highlighting their robust correlation decay.

Contribution

It establishes the non-singular influence of boundary conditions on these models, advancing understanding of their correlation decay properties.

Findings

Boundary conditions do not have a singular effect away from the boundary.

The models exhibit slow decay of correlations for local observables.

The results apply to the wired uniform spanning tree and temperleyan dimer model.

Abstract

Critical models are, almost by definition, supposed to feature both slow decay of correlations for local observables while retaining some mixing even for macroscopic observables. A strong version of the latter property is that changing boundary conditions cannot have a singular (in the measure theoretic sense) effect on the model away from the boundary, even asymptotically. In this paper we prove that statement for the wired uniform spanning tree and temperleyan dimer model.