Interacting growth processes and invariant percolation

Abstract

The aim of this paper is to underline the relation between reversible growth processes and invariant percolation. We present two models of interacting branching random walks (BRWs), truncated BRWs and competing BRWs, where survival of the growth process can be formulated as the existence of an infinite cluster in an invariant percolation on a tree. Our approach is fairly conceptual and allows generalizations to a wider set of "reversible" growth processes.

Published in at http://dx.doi.org/10.1214/13-AAP995 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (6)

• Unimodular Random Trees
• Survival, extinction and approximation of discrete-time branching random walks
• First passage percolation and competition models
• Percolation on a product of two trees
• Ecological equilibrium for restrained branching random walks
• Branching Random Walks on Free Products of Groups

Cited by in corpus (1)

• Branching random walks and multi-type contact-processes on the percolation cluster of ${\mathbb{Z}}^d$