7 papers
Small-ball estimates for random walks on groups
Tom Hutchcroft
We prove a new inequality bounding the probability that the random walk on a group has small total displacement in terms of the spectral and isoperimetric profiles of the group. Th…
Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation
Tom Hutchcroft
In long-range percolation on , we connect each pair of distinct points and by an edge independently at random with probability , whe…
The critical percolation probability is local
Philip Easo, Tom Hutchcroft
We prove Schramm's locality conjecture for Bernoulli bond percolation on transitive graphs: If is a sequence of infinite vertex-transitive graphs converging local…
Double-exponential susceptibility growth in Dyson's hierarchical model with interaction
Philip Easo, Tom Hutchcroft, Jana Kurrek
We study long-range percolation on the -dimensional hierarchical lattice, in which each possible edge is included independently at random with inclusion probability $1…
The number of ends in the uniform spanning tree for recurrent unimodular random graphs
Diederik van Engelenburg, Tom Hutchcroft
We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together…
Transience and anchored isoperimetric dimension of supercritical percolation clusters
Tom Hutchcroft
We establish several equivalent characterisations of the anchored isoperimetric dimension of supercritical clusters in Bernoulli bond percolation on transitive graphs. We deduce fr…