Geoffrey R. Grimmett

collaborators

5 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.PR2026

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.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

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…

math.CO2025

Non-self-touching paths in plane graphs

Geoffrey R. Grimmett

A path in a graph $G$ is called non-self-touching if two vertices are neighbours in the path if and only if they are neighbours in the graph. We investigate the existence of doubly…

Connective constants of Grigorchuk graphs

Coalescence in Markov chains

On counting polygons in a crystal

Alice and Bob on X: reversal, coupling, renewal

Non-self-touching paths in plane graphs

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