2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72936Let x and y be chosen uniformly in a graph G. We find the limiting distribution of the length of a loop-erased random walk from x to y on a large class of graphs that include the discrete torus in dimensions 5 and above. Moreover, on this family of graphs we show that a suitably normalized finite-dimensional scaling limit of the uniform spanning tree is a Brownian continuum random tree.6/6/05 version is substantially reorganized, with the main proof being more clearly presented as a proof by induction and the individual lemmas are now more self-containedProbability60D05 (Primary) 05C05, 60B99 (Secondary)text