The Annals of Applied Probability

Interacting growth processes and invariant percolation

Sebastian Müller

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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.

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Ann. Appl. Probab., Volume 25, Number 1 (2015), 268-286.

First available in Project Euclid: 16 December 2014

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Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 05C80: Random graphs [See also 60B20]

Survival interacting branching random walk invariant percolation unimodular random networks


Müller, Sebastian. Interacting growth processes and invariant percolation. Ann. Appl. Probab. 25 (2015), no. 1, 268--286. doi:10.1214/13-AAP995.

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