The maximum of branching Brownian motion in ${\mathbb{R}}^d$

Abstract

We show that in branching Brownian motion (BBM) in ${\mathbb{R}}^d$, $d\ge 2$, the law of $R_t^{\ast }$, the maximum distance of a particle from the origin at time $t$, converges as $t\to \infty$ to the law of a randomly shifted Gumbel random variable.

53 pages, 7 figures. Minor typos corrected. Final version, to appear in the Annals of Applied Probability

References in corpus (3)

• Maximal displacement in the $d$-dimensional branching Brownian motion
• Branching Brownian motion with selection
• Derivative martingale of the branching Brownian motion in dimension $d\ge 1$