  We establish an invariance principle for the barycenter of a Brunet-Derrida
particle system in $d$ dimensions. The model consists of $N$ particles
undergoing dyadic branching Brownian motion with rate $1$. At a branching
event, the number of particles is kept equal to $N$ by removing the particle
located furthest away from the barycenter. To prove the invariance principle, a
key step is to establish Harris recurrence for the process viewed from its
barycenter.
