29 citations · 200 across the 53 of their papers we have counts for
6 papers · 2 filters
Interlacements and the Wired Uniform Spanning Forest
Tom Hutchcroft
We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the cl…
Boundaries of Planar Graphs: A Unified Approach
Tom Hutchcroft, Yuval Peres
We give a new proof that the Poisson boundary of a planar graph coincides with the boundary of its square tiling and with the boundary of its circle packing, originally proven by G…
Indistinguishability of Trees in Uniform Spanning Forests
Tom Hutchcroft, Asaf Nachmias
We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible…
Collisions of Random Walks in Reversible Random Graphs
Tom Hutchcroft, Yuval Peres
We prove that in any recurrent reversible random rooted graph, two independent simple random walks started at the same vertex collide infinitely often almost surely. This applies t…
Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
Tom Hutchcroft
We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothe…
Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk
Omer Angel, Tom Hutchcroft, Asaf Nachmias +1
We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation…