Matthew C. H. Tointon

collaborators

5 papers

math.GR2025

Residually finite groups with uniformly almost flat quotients

David Guo, Matthew Tointon

We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obta…

math.CO2025

Small doubling implies small tripling for balls of large radius

Romain Tessera, Matthew Tointon

We show that if $K \geq 1$ is a parameter and $S$ is a finite symmetric subset of a group containing the identity such $∣ S^{2 n} ∣ \leq K ∣ S^{n} ∣$ for some integer $n \geq 2 K^{2}$ , then $|S^{3n}|…

math.PR2025

Spread-out percolation on transitive graphs of polynomial growth

Panagiotis Spanos, Matthew Tointon

Let $G$ be a vertex-transitive graph of superlinear polynomial growth. Given $r > 0$ , let $G_{r}$ be the graph on the same vertex set as $G$ , with two vertices joined by an edge if and…

math.MG2024

New bounds in the discrete analogue of Minkowski's second theorem

Matthew Tointon

We adapt an argument of Tao and Vu to show that if $I^»_{1} \leq \dots \leq I^»_{d}$ are the successive minima of an origin-symmetric convex body $K$ with respect to some lattice $Î<\mathbb{…

math.PR2024

Sharp relations between volume growth, isoperimetry and escape probability in vertex-transitive graphs

Romain Tessera, Matthew Tointon

We prove sharp bounds on the probability that the simple random walk on a vertex-transitive graph escapes the ball of radius $r$ before returning to its starting point. In particul…