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Interacting growth processes and invariant percolation. (English) Zbl 1308.60110
Summary: 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
05C80 Random graphs (graph-theoretic aspects)
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