The Annals of Probability

The Branching Annihilating Process: An Interacting Particle System

Aidan Sudbury

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Abstract

The branching annihilating process (BAP) is a special case of the branching annihilating walk of Bramson and Gray. In the BAP each particle places offspring on neighbouring sites at unit rate, but when two particles occupy the same site they annihilate each other. We show that the product measure with density 1/2 is the limit starting from any $A \neq \varnothing$. Also considered will be the DBAP (double BAP) in one dimension. In this model a particle always places offspring on both neighbouring sites. The limiting measure here depends critically on whether the initial number of particles is odd or even.

Article information

Source
Ann. Probab., Volume 18, Number 2 (1990), 581-601.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990846

Digital Object Identifier
doi:10.1214/aop/1176990846

Mathematical Reviews number (MathSciNet)
MR1055421

Zentralblatt MATH identifier
0705.60094

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Infinite particle system annihilation voter model

Citation

Sudbury, Aidan. The Branching Annihilating Process: An Interacting Particle System. Ann. Probab. 18 (1990), no. 2, 581--601. doi:10.1214/aop/1176990846. https://projecteuclid.org/euclid.aop/1176990846


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