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

Yuval Peres·David Revelle
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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.

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Yuval Peres, David Revelle. 2005-06-06. Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs. https://arxiv.org/abs/math/0410430

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