4 papers · 1 filter
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…