Sharif Digital Repository

The dimer model studies random dimer covers of a graph. A dimer cover is a subset of the edges of the graph such that each vertex is the endpoint of exactly one edge.The double-dimer model is a natural generalization of the dimer model, whose configuration is a union of two dimer covers, which ends up a set of even-length simple loops and doubled edges.The goal of this thesis is the study of statistical properties of very long doubledimer loops in very large lattices. To this end, we use the Grassmannian representation of the dimer model to compute some loop-related observables in rectangular domains of the square lattice, i.e. 1) the probability distribution of the number of nontrivial...