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