Tom Hutchcroft

activity

20162026

most citedThe critical two-point function for long-range percolation on the hierarchical lattice

5 citations · 10 across the 29 of their papers we have counts for

collaborators

Showing 2020 · math.PRShow all

7 papers · 2 filters

math.PR2020

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 $A$ i…

math.PR2020

Logarithmic corrections to scaling in the four-dimensional uniform spanning tree

Tom Hutchcroft, Perla Sousi

We compute the precise logarithmic corrections to mean-field scaling for various quantities describing the uniform spanning tree of the four-dimensional hypercubic lattice $\mathbb…

math.PR2020

Collisions of Random Walks in Dynamic Random Environments

Noah Halberstam, Tom Hutchcroft

We study dynamic random conductance models on $Z^{2}$ in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove un…

math.PR2020

Power-law bounds for critical long-range percolation below the upper-critical dimension

Tom Hutchcroft

We study long-range Bernoulli percolation on $Z^{d}$ in which each two vertices $x$ and $y$ are connected by an edge with probability $1 - exp (- β ∥ x - y ∥^{- d - α})$ . It is a the…

math.PR2020

Continuity of the Ising phase transition on nonamenable groups

Tom Hutchcroft

We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gi…

math.PR2020

On the tail of the branching random walk local time

Omer Angel, Tom Hutchcroft, Antal A. Járai

Consider a critical branching random walk on $Z^{d}$ , $d \geq 1$ , started with a single particle at the origin, and let $L (x)$ be the total number of particles that ever visi…