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Scaling limits of random spanning trees
Abstract
A spanning tree of a finite connected graph G is a connected subgraph of G that contains every vertex and contains no cycles. A well-known result of Aldous states that the scaling limit of a uniformly chosen spanning tree of the complete graph is the Brownian tree (CRT). In fact, this statement is more general: the Brownian tree is the scaling limit of uniform spanning trees for a large set of high-dimensional graphs. In this talk, we'll try to explain this universal phenomenon. Time permitting, we will also discuss the scaling limits of non-uniform random spanning trees. Based on joint works with Asaf Nachmias and Matan Shalev.
