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Finite particle systems and infection models

Published online by Cambridge University Press:  24 October 2008

Peter Donnelly  and
Dominic Welsh
Peter Donnelly
Affiliation:
Balliol College, Oxford
Dominic Welsh
Affiliation:
Merton College, Oxford
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Extract

Infinite particle systems on lattices have been extensively studied in recent years. The main questions of interest concern the ergodic and limiting behaviour of these processes, and their relationship with the dimension of the underlying lattice. A comprehensive review is given by Durrett(6).

One of the more tractable of these processes is the voter model introduced by Clifford and Sudbury(3) and much studied since, see for example the monograph by Griffeath(8), or the papers by Harris(11), Holley and Liggett(13), Bramson and Griffeath(1) and (2) or, for a more general approach, Kelly(16).

In this paper we consider the case where the underlying spatial structure is finite and examine the transient behaviour of the voter process and also the infection process introduced by Williams and Bjerknes(21).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 1 , July 1983 , pp. 167 - 182
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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