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The biased annihilating branching process

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Claudia Neuhauser  and
Aidan Sudbury
Claudia Neuhauser*
Affiliation:
University of Southern California
Aidan Sudbury*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, USA. Partially supported by the National Science Foundation.
∗∗Postal address: Mathematics Department, Monash University, Clayton, VIC 3168, Australia.
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Abstract

In the biased annihilating branching process, particles place offspring on empty neighboring sites at rate A and destroy neighbors at rate 1. It is conjectured that for any λ ≥ 0 the population will spread to ∞, and this is shown in one dimension for The process on a finite graph when starting with a non-empty configuration has limiting distribution vλ /(λ +1), the product measure with density λ/(1 +λ). It is shown that vλ /(λ +1) and δ Ø are the only stationary distributions on Moreover, if and the initial configuration is non-empty, then the limiting measure is vλ /(λ +1) provided the initial measure converges.

Keywords

INFINITE PARTICLE SYSTEMANNIHILATION

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 24 - 38
Copyright
Copyright © Applied Probability Trust 1993 

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