BRANCHING EXCLUSION PROCESS ON A STRIP

摘要

We consider a model of stochastically interacting particles on an infinite strip of Z(2); in this model, known as a branching exclusion process, particles jump to each empty neighboring site with rate lambda/4 and also can create a new particle with rate 1/4 at each one of these sites. The initial configuration is assumed to have a rightmost particle and we study the process as seen from the rightmost vertical line occupied. We prove that this process has exactly one invariant measure with the property that H, the number of empty sites to the left of the rightmost particle, has an exponential moment. This refines a result presented by Bramson er nl., who proved that for d = I, H is finite with probability 1. [References: 17]