Geoffrey R. Grimmett

activity

20242026

collaborators

4 papers

math.CO2026

Connective constants of Grigorchuk graphs

Geoffrey R. Grimmett

The connective constant $μ (G)$ of a graph $G$ is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. We prove upper and lower bounds for th…

math.CO2026

On counting polygons in a crystal

Geoffrey R. Grimmett

How many $n$ -step polygons exist that contain a given vertex of an infinite quasi-transitive graph $G$ ? The exponential growth rate of such polygons is identified as the connective…

math.PR2025

Coalescence in Markov chains

Geoffrey R. Grimmett, Mark Holmes

A Markov chain $X^{i}$ on a finite state space $S$ has transition matrix $P$ and initial state $i$ . We may run the chains $(X^{i} : i \in S)$ in parallel, while insisting that any two su…

math.PR2024

Alice and Bob on $X$ : reversal, coupling, renewal

Geoffrey R. Grimmett

A neat question involving coin flips surfaced on $X$ , and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at…

Connective constants of Grigorchuk graphs

On counting polygons in a crystal

Coalescence in Markov chains

Alice and Bob on X: reversal, coupling, renewal

Alice and Bob on $X$ : reversal, coupling, renewal