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The survival of various interacting particle systems

Part of:Special processes

Published online by Cambridge University Press:  01 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University
*
* Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
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Abstract

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Particles may be removed from a lattice by murder, coalescence, mutual annihilation and simple death. If the particle system is not to die out, the removed particles must be replaced by births. This letter shows that coalescence can be counteracted by arbitrarily small birth-rates and contrasts this with the situations for annihilation and pure death where there are critical phenomena. The problem is unresolved for murder.

Keywords

INFINITE PARTICLE SYSTEMANNIHILATIONCONTACT PROCESS

MSC classification

Primary:60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Letter to the Editor
Information
Advances in Applied Probability , Volume 25 , Issue 4 , December 1993, pp. 1010 - 1012
Copyright
Copyright © Applied Probability Trust 1993 

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