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The annihilating process

Published online by Cambridge University Press:  14 July 2016

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: [email protected]

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.

Type
Research Papers
Copyright
Copyright © by the Applied Probability Trust 2001 

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