## The Annals of Applied Probability

### Interacting growth processes and invariant percolation

Sebastian Müller

#### 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

https://projecteuclid.org/euclid.aoap/1418740186

Digital Object Identifier
doi:10.1214/13-AAP995

Mathematical Reviews number (MathSciNet)
MR3297773

Zentralblatt MATH identifier
1308.60110

#### 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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