2 citations · 2 across the 5 of their papers we have counts for
6 papers
Connective constants of Grigorchuk graphs
Geoffrey R. Grimmett
The connective constant of a graph 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…
On counting polygons in a crystal
Geoffrey R. Grimmett
How many -step polygons exist that contain a given vertex of an infinite quasi-transitive graph ? The exponential growth rate of such polygons is identified as the connective…
Coalescence in Markov chains
Geoffrey R. Grimmett, Mark Holmes
A Markov chain on a finite state space has transition matrix and initial state . We may run the chains in parallel, while insisting that any two su…
Alice and Bob on : reversal, coupling, renewal
Geoffrey R. Grimmett
A neat question involving coin flips surfaced on , and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at…
Dominic Welsh (1938-2023)
Geoffrey R. Grimmett
This biographical and scientific memoir of Dominic Welsh includes summaries of his important contributions to probability and combinatorics. With John Hammersley, he introduced fir…
Non-self-touching paths in plane graphs
Geoffrey R. Grimmett
A path in a graph 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…