29 citations · 200 across the 53 of their papers we have counts for
5 papers · 1 filter
Non-intersection of transient branching random walks
Tom Hutchcroft
Let be a Cayley graph of a nonamenable group with spectral radius . It is known that branching random walk on with offspring distribution is transient, i.e., visi…
Large, lengthy graphs look locally like lines
Itai Benjamini, Tom Hutchcroft
We apply the theory of unimodular random rooted graphs to study the metric geometry of large, finite, bounded degree graphs whose diameter is proportional to their volume. We prove…
Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution
Jonathan Hermon, Tom Hutchcroft
Let be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on . We prove that if is nonamenable and then there exists a p…
The boundedness condition in nonamenable percolation
Tom Hutchcroft
Let be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on . In recent work, we conjectured that if is nonamenable then the m…
New critical exponent inequalities for percolation and the random cluster model
Tom Hutchcroft
We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin-Kasteley…