On the boundary at infinity for branching random walk

Candellero Elisabetta, Roma Tre University

We introduce an original connection between branching random walk on a graph and the Martin boundary for the underlying random walk. More precisely, we prove that when the graph is transient, supercritical branching random walk converges almost surely (under rescaling) to a random measure on the Martin boundary of the graph. Based on \cite{CH23}, a joint work with Tom Hutchcroft (Caltech). A similar result was also obtained at the same time and independently by \cite{KW22}.

Area: IS16 - Random walks and disordered models (Niccolò Torri)

Keywords: Branching random walks, Martin boundary

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