Translator Disclaimer
2015 Dependent double branching annihilating random walk
Marton Balazs, Attila Nagy
Author Affiliations +
Electron. J. Probab. 20: 1-32 (2015). DOI: 10.1214/EJP.v20-4045


Double (or parity conserving) branching annihilating random walk, introduced by Sudbury in '90, is a one-dimensional non-attractive particle system in which positive and negative particles perform nearest neighbor hopping, produce two offsprings to neighboring lattice points and annihilate when they meet. Given an odd number of initial particles, positive recurrence as seen from the leftmost particle position was first proved by Belitsky, Ferrari, Menshikov and Popov in '01 and, subsequently in a much more general setup, in the article by Sturm and Swart (Tightness of voter model interfaces) in '08. These results assume that jump rates of the various moves do not depend on the configuration of the particles not involved in these moves. The present article deals with the case when the jump rates are affected by the locations of several particles in the system. Motivation for such models comes from non-attractive interacting particle systems with particle conservation. Under suitable assumptions we establish the existence of the process, and prove that the one-particle state is positive recurrent. We achieve this by arguments similar to those appeared in the previous article by Sturm and Swart. We also extend our results to some cases of long range jumps, when branching can also occur to non-neighboring sites. We outline and discuss several particular examples of models where our results apply.


Download Citation

Marton Balazs. Attila Nagy. "Dependent double branching annihilating random walk." Electron. J. Probab. 20 1 - 32, 2015.


Accepted: 13 August 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1329.60327
MathSciNet: MR3383568
Digital Object Identifier: 10.1214/EJP.v20-4045

Primary: 60K35


Vol.20 • 2015
Back to Top