29 citations · 200 across the 53 of their papers we have counts for
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Critical cluster volumes in hierarchical percolation
Tom Hutchcroft
We consider long-range Bernoulli bond percolation on the -dimensional hierarchical lattice in which each pair of points and are connected by an edge with probability $1-…
Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
Noah Halberstam, Tom Hutchcroft
We compute the precise logarithmic corrections to Alexander-Orbach behaviour for various quantities describing the geometric and spectral properties of the four-dimensional uniform…
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…
Slightly supercritical percolation on nonamenable graphs II: Growth and isoperimetry of infinite clusters
Tom Hutchcroft
We study the growth and isoperimetry of infinite clusters in slightly supercritical Bernoulli bond percolation on transitive nonamenable graphs under the boundedness conditio…
On the boundary at infinity for branching random walk
Elisabetta Candellero, Tom Hutchcroft
We prove that supercritical branching random walk on a transient graph converges almost surely under rescaling to a random measure on the Martin boundary of the graph. Several open…
Most transient random walks have infinitely many cut times
Noah Halberstam, Tom Hutchcroft
We prove that if is a random walk on a transient graph such that the Green's function decays at least polynomially along the random walk, then h…
Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on
Tom Hutchcroft
Consider long-range Bernoulli percolation on in which we connect each pair of distinct points and by an edge with probability , whe…