Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs

Abstract

Let 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-contained

Cited by in corpus (6)

• The local weak limit of the minimum spanning tree of the complete graph
• Interlacements and the Wired Uniform Spanning Forest
• Logarithmic corrections to scaling in the four-dimensional uniform spanning tree
• Rayleigh processes, real trees, and root growth with re-grafting
• Random graph asymptotics on high-dimensional tori
• Critical random graphs: limiting constructions and distributional properties