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The binary branching Brownian motion in the boundary case is a particlesystem on the real line behaving as follows. It starts with a unique particlepositioned at the origin at time $0$. The particle moves according to aBrownian motion with drift $\mu = 2$ and diffusion coefficient $\sigma^2 = 2$,until an independent exponential time of parameter $1$. At that time, theparticle dies giving birth to two children who then start independent copies ofthe same process from their birth place. It is well-known that in this system,the cloud of particles eventually drifts to $\infty$. The aim of this note isto provide a precise estimate for the total number of particles that were bornon the negative half-line, investigating in particular the tail decay of thisrandom variable.

Total number of births on the negative half-line of the binary branching Brownian motion in the boundary case