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The annihilating process on random trees and the square lattice

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University
*
∗ Postal address: School of Mathematical Sciences, Monash University, PO Box 28M, VIC 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. The survival probability is calculated for a random tree and for the square lattice. A connection is made between annihilating processes and the adsorption of molecules onto surfaces. A one-dimensional adsorption problem is solved in the case in which the two neighbours do not act independently.

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 41 , Issue 3 , September 2004 , pp. 816 - 831
Copyright
Copyright © Applied Probability Trust 2004 

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References

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