The double-dimer nesting field converges to the CLE(4) nesting field in Sobolev spaces as the mesh size tends to zero, and the local loop count satisfies a central limit theorem.
Does a portion of dimer configuration determines its domain of definition?
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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.
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Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4)
The double-dimer nesting field converges to the CLE(4) nesting field in Sobolev spaces as the mesh size tends to zero, and the local loop count satisfies a central limit theorem.