Maximal displacement in the $d$-dimensional branching Brownian motion
Résumé
We consider a branching Brownian motion evolving in R d. We prove that the asymptotic behaviour of the maximal displacement is given by a first ballistic order, plus a logarithmic correction that increases with the dimension d. The proof is based on simple geometrical evidence. It leads to the interesting following side result: with high probability, for any d ≥ 2, individuals on the frontier of the process are close parents if and only if they are geographically close.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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