Limiting laws of supercritical branching random walks
نویسندگان
چکیده
In this note, we make explicit the limit law of the renormalized supercritical branching random walk, giving credit to a conjecture formulated in [5] for a continuous analogue of the branching random walk. Also, in the case of a branching random walk on a homogeneous tree, we express the law of the corresponding limiting renormalized Gibbs measures, confirming, in this discrete model, conjectures formulated by physicists about the Poisson-Dirichlet nature of the jumps in the limit, and precising the conjecture by giving the spatial distribution of these jumps.
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