Tom Hutchcroft

activity

20152026

most citedUnimodular Hyperbolic Triangulations: Circle Packing and Random Walk

29 citations · 200 across the 53 of their papers we have counts for

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Showing 2018Show all

8 papers · 1 filter

math.PR2018

Indistinguishability of collections of trees in the uniform spanning forest

Tom Hutchcroft

We prove the following indistinguishability theorem for $k$ -tuples of trees in the uniform spanning forest of $Z^{d}$ : Suppose that $A$ is a property of a $k$ -tupl…

math.GR2018

Kazhdan groups have cost 1

Tom Hutchcroft, Gábor Pete

We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.

math.PR2018

No percolation at criticality on certain groups of intermediate growth

Jonathan Hermon, Tom Hutchcroft

We prove that critical percolation has no infinite clusters almost surely on any unimodular quasi-transitive graph satisfying a return probability upper bound of the form $p_n(v,v)…

math.PR2018

Locality of the critical probability for transitive graphs of exponential growth

Tom Hutchcroft

Around 2008, Schramm conjectured that the critical probabilities for Bernoulli bond percolation satisfy the following continuity property: If $(G_{n})_{n \geq 1}$ is a sequence of tra…

math.PR2018

Anomalous diffusion of random walk on random planar maps

Ewain Gwynne, Tom Hutchcroft

We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most $n^{1/4 + o_{n} (1)}$ in $n$ units of time. Together…

math.PR2018

Percolation on hyperbolic graphs

Tom Hutchcroft

We prove that Bernoulli bond percolation on any nonamenable, Gromov hyperbolic, quasi-transitive graph has a phase in which there are infinitely many infinite clusters, verifying a…

math.PR2018

Universality of high-dimensional spanning forests and sandpiles

Tom Hutchcroft

We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very large class of graphs, including every transitive graph of at least quintic volume growth an…

math.PR2018★ 10 cited

Mallows permutations as stable matchings

Omer Angel, Alexander E. Holroyd, Tom Hutchcroft +1

We show that the Mallows measure on permutations of $1, \dots, n$ arises as the law of the unique Gale-Shapley stable matching of the random bipartite graph conditioned to be perfec…