29 citations · 200 across the 53 of their papers we have counts for
7 papers · 1 filter
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 i…
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…
Collisions of Random Walks in Dynamic Random Environments
Noah Halberstam, Tom Hutchcroft
We study dynamic random conductance models on in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove un…
Power-law bounds for critical long-range percolation below the upper-critical dimension
Tom Hutchcroft
We study long-range Bernoulli percolation on in which each two vertices and are connected by an edge with probability . It is a the…
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…
On the tail of the branching random walk local time
Omer Angel, Tom Hutchcroft, Antal A. Járai
Consider a critical branching random walk on , , started with a single particle at the origin, and let be the total number of particles that ever visi…
Slightly supercritical percolation on nonamenable graphs I: The distribution of finite clusters
Tom Hutchcroft
We study the distribution of finite clusters in slightly supercritical () Bernoulli bond percolation on transitive nonamenable graphs, proving in particular that…