  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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