  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.
