Uniform Spanning Forests
Russell Lyons, Yuval Peres · Cambridge University Press eBooks · 2016
Abstract. It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience. §1. Introduction. The area of uniform spanning forests has proved to be very fertile. It has important connections to several areas, such as random walks, algorithms, domino tilings, electrical networks, and potential theory. It led to the discovery of the SLE processes, which are a major theme of contemporary research in planar stochastic processes. Although much