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