Matthew C. H. Tointon

activity

20122024

most citedCommuting probabilities of infinite groups

13 citations · 29 across the 17 of their papers we have counts for

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3 papers · 1 filter

math.PR2024

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.PR2021★ 2 cited

Non-triviality of the phase transition for percolation on finite transitive graphs

Tom Hutchcroft, Matthew Tointon

We prove that if $(G_{n})_{n \geq 1} = ((V_{n}, E_{n}))_{n \geq 1}$ is a sequence of finite, vertex-transitive graphs with bounded degrees and $∣ V_{n} ∣ \to \infty$ that is at least $(1 + ε)$ -dimensi…

math.PR2020★ 1 cited

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…