29 citations · 33 across the 6 of their papers we have counts for
8 papers
Flows and ferromagnets
Geoffrey Grimmett
The two-point correlation function of a Potts model on a graph may be expressed in terms of the flow polynomials of `Poissonian' random graphs derived from by replacing eac…
Influence and sharp-threshold theorems for monotonic measures
B. T. Graham, G. R. Grimmett
The influence theorem for product measures on the discrete space {0,1}^N may be extended to probability measures with the property of monotonicity (which is equivalent to `strong p…
Uniqueness and multiplicity of infinite clusters
Geoffrey Grimmett
The Burton--Keane theorem for the almost-sure uniqueness of infinite clusters is a landmark of stochastic geometry. Let be a translation-invariant probability measure with the…
Branching Processes, and Random-Cluster Measures on Trees
Geoffrey Grimmett, Svante Janson
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite path…
Negative association in uniform forests and connected graphs
G. R. Grimmett, S. N. Winkler
We consider three probability measures on subsets of edges of a given finite graph , namely those which govern, respectively, a uniform forest, a uniform spanning tree, and a un…
On smallest triangles
Geoffrey Grimmett, Svante Janson
Pick n points independently at random in R^2, according to a prescribed probability measure mu, and let D^n_1 <= D^n_2 <= ... be the areas of the binomial n choose 3 triangles thus…