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

25 citations · 25 across the 3 of their papers we have counts for

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math.PR2004★ 25 cited

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

Yuval Peres, David Revelle

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 d…

math.PR2004

Mixing times for random walks on finite lamplighter groups

Yuval Peres, David Revelle

Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up…

math.PR2003

Instability of set recurrence and Green's function on groups with the Liouville property

Itai Benjamini, David Revelle

Let and be probability measures on a group Γand let G_μand G_νdenote Green's function with respect to μand ν. The group Γis said to admit instability of Green's function if…