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Critical models are, almost by definition, supposed to feature both slowdecay of correlations for local observables while retaining some mixing evenfor macroscopic observables. A strong version of the latter property is thatchanging boundary conditions cannot have a singular (in the measure theoreticsense) effect on the model away from the boundary, even asymptotically. In thispaper we prove that statement for the wired uniform spanning tree andtemperleyan dimer model.

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