G. Grimmett

Publications
Influence

G. Grimmett, D. Stirzaker
Mathematics
1 March 2002

Events and their probabilities random variables and their distributions discrete random variables continuous random variables generating functions and their applications Markov chains convergence of… Expand

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The shortest-path problem for graphs with random arc-lengths

A. Frieze, G. Grimmett
Mathematics, Computer Science
Discret. Appl. Math.
1985

We consider the problem of finding the shortest distance between all pairs of vertices in a complete digraph on n vertices, whose arc-lengths are non-negative random variables. Expand

Influence and sharp-threshold theorems for monotonic measures

B. Graham, G. Grimmett
Mathematics
3 May 2005

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 positive… Expand

Cluster detection in networks using percolation

Ery Arias-Castro, G. Grimmett
Mathematics
2 April 2011

We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental… Expand

An upper bound for the number of spanning trees of a graph

G. Grimmett
Mathematics, Computer Science
Discret. Math.
1 December 1976

Strict inequality for critical values of Potts models and random-cluster processes

C. Bezuidenhout, G. Grimmett, H. Kesten
Mathematics
1 November 1993

We prove that the critical value βc of a ferromagnetic Potts model is astrictly decreasing function of the strengths of interaction of the process. This is achieved in the (more) general context of… Expand

On the Number of Clusters in the Percolation Model

G. Grimmett
Mathematics
1 June 1976

Locality of connective constants

G. Grimmett, Zhongyang Li
Mathematics, Physics
Discret. Math.
29 November 2014

We prove a locality theorem for connective constants, namely, that the connective constant of two graphs are close in value whenever the graphs agree on a large ball around the origin (and a further condition is satisfied). Expand

Entanglement in the Quantum Ising Model

G. Grimmett, T. Osborne, P. Scudo
Mathematics, Physics
23 April 2007

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong,… Expand

Lipschitz percolation

N. Dirr, P. Dondl, G. Grimmett, A. Holroyd, M. Scheutzow
Mathematics
17 November 2009

We prove the existence of a (random) Lipschitz function F : Z → Z such that, for every x ∈ Z, the site (x, F (x)) is open in a site percolation process on Z. The Lipschitz constant may be taken to be… Expand

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