29 citations · 200 across the 53 of their papers we have counts for
7 papers · 1 filter
Supercritical percolation on finite transitive graphs I: Uniqueness of the giant component
Philip Easo, Tom Hutchcroft
Let be a sequence of finite, connected, vertex-transitive graphs with volume tending to infinity. We say that a sequence of parameters $…
The bunkbed conjecture holds in the limit
Tom Hutchcroft, Petar Nizić-Nikolac, Alexander Kent
Let be a countable graph. The Bunkbed graph of is the product graph , which has vertex set with "horizontal'' edges inherited from …
High-dimensional near-critical percolation and the torus plateau
Tom Hutchcroft, Emmanuel Michta, Gordon Slade
We consider percolation on and on the -dimensional discrete torus, in dimensions for the nearest-neighbour model and in dimensions for spread-out…
What are the limits of universality?
Noah Halberstam, Tom Hutchcroft
It is a central prediction of renormalisation group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and…
On the derivation of mean-field percolation critical exponents from the triangle condition
Tom Hutchcroft
We give a new derivation of mean-field percolation critical behaviour from the triangle condition that is quantitatively much better than previous proofs when the triangle diagram…
Non-triviality of the phase transition for percolation on finite transitive graphs
Tom Hutchcroft, Matthew Tointon
We prove that if is a sequence of finite, vertex-transitive graphs with bounded degrees and that is at least -dimensi…
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…