Maximal displacement in the $d$-dimensional branching Brownian motion

Abstract

We consider a branching Brownian motion evolving in ${\mathbb{R}}^d$. 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 $d\ge 2$, individuals on the frontier of the process are close parents if and only if they are geographically close.

12 pages, 2 figures

References in corpus (2)

• Minima in branching random walks
• Maximal displacement in a branching random walk through interfaces

Cited by in corpus (6)

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• The maximum of branching Brownian motion in ${\mathbb{R}}^d$
• Derivative martingale of the branching Brownian motion in dimension $d\ge 1$
• Spread rate of branching Brownian motions