Loop statistics for dimer models on the torus
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A dimer configuration of a graph G is a subset of edges such that every
vertex of G is adjacent to exactly one edge of this subset. If we
superimpose two dimer configurations of the same graph, we get double edges
and loops. When G is a large piece of a periodic graph drawn on the torus,
these loops can wind around the torus non trivially. We derive the limiting
law, when the size of the mesh of G goes to zero, of the winding number of
this family of loop when the two configurations are sampled at random from a
Gibbs measure.
This talk is part of the Probability series.
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