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

collaborators

74 papers

math.PR2026

Super-Brownian limits and the $k$ -point function for high-dimensional percolation

Arthur Blanc-Renaudie, Tom Hutchcroft

We prove that there exist positive constants $A$ and $V$ such that the high-dimensional critical percolation $k$ -point function is given by \[ T_{p_c}(x_1,x_2,\ldots,x_{k}) \sim V^…

math.PR2025

A discontinuous percolation phase transition on the hierarchical lattice

Johannes Bäumler, Tom Hutchcroft

For long-range percolation on $Z$ with translation-invariant edge kernel $J$ , it is a classical theorem of Aizenman and Newman (1986) that the phase transition is disconti…

math.DG2025

Transitive graphs of non-negative Ollivier-Ricci curvature have polynomial growth

Camillo Brena, Tom Hutchcroft, Florentin Münch

We prove that every transitive graph of non-negative Ollivier-Ricci curvature has polynomial growth. We deduce from this and a theorem of Brena and Brue that a finitely generated g…

math-ph2025

Dimension dependence of critical phenomena in long-range percolation

Tom Hutchcroft

Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of t…

math.PR2025

Critical long-range percolation III: The upper critical dimension

Tom Hutchcroft

In long-range percolation on $Z^{d}$ , points $x$ and $y$ are connected by an edge with probability $1 - exp (- β ∥ x - y ∥^{- d - α})$ , where $α > 0$ is fixed and $β \geq 0$ is a parame…

math.PR2025

Critical long-range percolation II: Low effective dimension

Tom Hutchcroft

In long-range percolation on $Z^{d}$ , points $x$ and $y$ are connected by an edge with probability $1 - exp (- β ∥ x - y ∥^{- d - α})$ , where $α > 0$ is fixed and $β \geq 0$ is a parame…

math.PR2025

Critical long-range percolation I: High effective dimension

Tom Hutchcroft

In long-range percolation on $Z^{d}$ , points $x$ and $y$ are connected by an edge with probability $1 - exp (- β ∥ x - y ∥^{- d - α})$ , where $α > 0$ is fixed and $β \geq 0$ is a parame…

math.PR2024

Dimension jump at the uniqueness threshold for percolation in $\infty + d$ dimensions

Tom Hutchcroft, Minghao Pan

Consider percolation on $T \times Z^{d}$ , the product of a regular tree of degree $k \geq 3$ with the hypercubic lattice $Z^{d}$ . It is known that this graph has $0<p_c…

math.PR2024

A relation between isoperimetry and total variation decay with applications to graphs of non-negative Ollivier-Ricci curvature

Tom Hutchcroft, Isaac M. Lopez

We prove an inequality relating the isoperimetric profile of a graph to the decay of the random walk total variation distance $\sup_{x\sim y} ||P^n(x,\cdot)-P^n(y,\cdot)||_{\mathrm…

math.GR2024

Infinite stationary measures of co-compact group actions

Mohammedsaid Alhalimi, Tom Hutchcroft, Minghao Pan +2

Let $Γ$ be a finitely generated group, and let $μ$ be a nondegenerate, finitely supported probability measure on $Γ$ . We show that every co-compact $Γ$ action on a locally compact…

math.PR2024

Percolation at the uniqueness threshold via subgroup relativization

Tom Hutchcroft, Minghao Pan

We study percolation on nonamenable groups at the uniqueness threshold $p_{u}$ , the critical value that separates the phase in which there are infinitely many infinite clusters from…

math.PR2024

Small-ball estimates for random walks on groups

Tom Hutchcroft

We prove a new inequality bounding the probability that the random walk on a group has small total displacement in terms of the spectral and isoperimetric profiles of the group. Th…

math.PR2024

Proof of the Diaconis--Freedman Conjecture on partially-exchangeable processes

Noah Halberstam, Tom Hutchcroft

We prove a conjecture of Diaconis and Freedman (Ann. Probab. 1980) characterising the extreme points of the set of partially-exchangeable processes on a countable set. More concret…

math.PR2024

Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation

Tom Hutchcroft

In long-range percolation on $Z^{d}$ , we connect each pair of distinct points $x$ and $y$ by an edge independently at random with probability $1 - exp (- β ∥ x - y ∥^{- d - α})$ , whe…

math.PR2023★ 1 cited

Thick points of 4D critical branching Brownian motion

Nathanaël Berestycki, Tom Hutchcroft, Antoine Jego

We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension $d = 4$ . We determine the e…

math.PR2023

The critical percolation probability is local

Philip Easo, Tom Hutchcroft

We prove Schramm's locality conjecture for Bernoulli bond percolation on transitive graphs: If $(G_{n})_{n \geq 1}$ is a sequence of infinite vertex-transitive graphs converging local…

math.GR2023

Uniform finite presentation for groups of polynomial growth

Philip Easo, Tom Hutchcroft

We prove a quantitative refinement of the statement that groups of polynomial growth are finitely presented. Let $G$ be a group with finite generating set $S$ and let $\operatornam…

math.PR2023★ 3 cited

Uniqueness of the infinite tree in low-dimensional random forests

Noah Halberstam, Tom Hutchcroft

The arboreal gas is the random (unrooted) spanning forest of a graph in which each forest is sampled with probability proportional to $β^{# edges}$ for some $β \geq 0$ , whic…

math.PR2023

Double-exponential susceptibility growth in Dyson's hierarchical model with $∣ x - y ∣^{- 2}$ interaction

Philip Easo, Tom Hutchcroft, Jana Kurrek

We study long-range percolation on the $d$ -dimensional hierarchical lattice, in which each possible edge ${x, y}$ is included independently at random with inclusion probability $1…

math.PR2023

The number of ends in the uniform spanning tree for recurrent unimodular random graphs

Diederik van Engelenburg, Tom Hutchcroft

We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together…

math.PR2022★ 1 cited

Critical cluster volumes in hierarchical percolation

Tom Hutchcroft

We consider long-range Bernoulli bond percolation on the $d$ -dimensional hierarchical lattice in which each pair of points $x$ and $y$ are connected by an edge with probability $1-…

math.PR2022

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…

math.PR2022

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…

math.PR2022

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 $L^{2}$ boundedness conditio…

Super-Brownian limits and the k-point function for high-dimensional percolation

A discontinuous percolation phase transition on the hierarchical lattice

Transitive graphs of non-negative Ollivier-Ricci curvature have polynomial growth

Dimension dependence of critical phenomena in long-range percolation

Critical long-range percolation III: The upper critical dimension

Critical long-range percolation II: Low effective dimension

Critical long-range percolation I: High effective dimension

Dimension jump at the uniqueness threshold for percolation in ∞+d dimensions

A relation between isoperimetry and total variation decay with applications to graphs of non-negative Ollivier-Ricci curvature

Infinite stationary measures of co-compact group actions

Percolation at the uniqueness threshold via subgroup relativization

Small-ball estimates for random walks on groups

Proof of the Diaconis--Freedman Conjecture on partially-exchangeable processes

Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation

Thick points of 4D critical branching Brownian motion

The critical percolation probability is local

Uniform finite presentation for groups of polynomial growth

Uniqueness of the infinite tree in low-dimensional random forests

Double-exponential susceptibility growth in Dyson's hierarchical model with ∣x−y∣−2 interaction

The number of ends in the uniform spanning tree for recurrent unimodular random graphs

Critical cluster volumes in hierarchical percolation

Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree

Transience and anchored isoperimetric dimension of supercritical percolation clusters

Slightly supercritical percolation on nonamenable graphs II: Growth and isoperimetry of infinite clusters

Super-Brownian limits and the $k$ -point function for high-dimensional percolation

Dimension jump at the uniqueness threshold for percolation in $\infty + d$ dimensions

Double-exponential susceptibility growth in Dyson's hierarchical model with $∣ x - y ∣^{- 2}$ interaction