UVictoria Probability and Dynamics Seminar: Gourab Ray

Double dimers are superimposition of two perfect matchings. Such superimpositions can be decomposed into disjoint simple loops. The question we address is: as the graphs become large, in a 'typical' double dimer sample, do some of the loops diverge to an infinite loop (or a bi-infinite path)? It is known that in the square lattice, this is not the case. In this talk, I will address the same question, but on planar hyperbolic graphs. (I will not spoil the answer in the abstract! )

The answer involves elements from the theory of hyperbolic geometry, circle packings, spanning trees, random walks and unimodular random graphs.