The Annals of Applied Probability

Interacting growth processes and invariant percolation

Sebastian Müller

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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.

Article information

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

Dates
First available in Project Euclid: 16 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1418740186

Digital Object Identifier
doi:10.1214/13-AAP995

Mathematical Reviews number (MathSciNet)
MR3297773

Zentralblatt MATH identifier
1308.60110

Subjects
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]

Keywords
Survival interacting branching random walk invariant percolation unimodular random networks

Citation

Müller, Sebastian. Interacting growth processes and invariant percolation. Ann. Appl. Probab. 25 (2015), no. 1, 268--286. doi:10.1214/13-AAP995. https://projecteuclid.org/euclid.aoap/1418740186


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