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The annihilating process

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Martin O'Hely  and
Aidan Sudbury
Martin O'Hely*
Affiliation:
University of Oregon
Aidan Sudbury*
Affiliation:
Monash University
*
∗ Postal address: Department of Biology, University of Oregon, Engene, OR 97403, USA.
∗∗ Postal address: Department of Mathematics and Statistics, Monash University, PO Box 28M, Victoria 3800, Australia. Email address: aidan.sudbury@sci.monash.edu.au
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Abstract

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. It is shown that with initial configuration ℤ the distribution of particles at all times is a renewal process and that the probability that a site remains occupied for all time tends to 1/e. Time-dependent behaviour is also calculated for the tree 𝕋r .

Keywords

infinite particle systemannihilation

MSC classification

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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 223 - 231
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

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