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.
Tau-functions ` a la Dub´ edat and probabilities of cylindrical events for double-dimers and CLE(4)
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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.