5 citations · 6 across the 7 of their papers we have counts for
23 papers · 1 filter
Percolation at the uniqueness threshold via subgroup relativization
Tom Hutchcroft, Minghao Pan
We study percolation on nonamenable groups at the uniqueness threshold , the critical value that separates the phase in which there are infinitely many infinite clusters from…
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-…
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…
The critical two-point function for long-range percolation on the hierarchical lattice
Tom Hutchcroft
We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the -dimensional hierarchical la…
Transience and recurrence of sets for branching random walk via non-standard stochastic orders
Tom Hutchcroft
We study how the recurrence and transience of space-time sets for a branching random walk on a graph depends on the offspring distribution. Here, we say that a space-time set i…