Abstract
Double (or parity conserving) branching annihilating random walk, introduced by Sudbury in '90, is a onedimensional nonattractive 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 nonattractive interacting particle systems with particle conservation. Under suitable assumptions we establish the existence of the process, and prove that the oneparticle 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 nonneighboring sites. We outline and discuss several particular examples of models where our results apply.
Original language  English 

Article number  84 
Pages (fromto)  132 
Number of pages  32 
Journal  Electronic Journal of Probability 
Volume  20 
DOIs  
Publication status  Published  13 Aug 2015 
Keywords
 nonattractive particle system
 double branching annihilating random walk
 parity conserving
 long range dependent rates
 long range branching
 positive recurrence
 interface tightness
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Professor Marton Balazs
 School of Mathematics  Professor of Probability
 Probability, Analysis and Dynamics
 Probability
Person: Academic , Member