Poissonian statistics in the extremal process of branching Brownian motion

Understand

As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm.

• Pure Appl.
• Math.
• 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles descend with overwhelming probability from ancestors having split either within a distance of order 1 from time 0, or within a distance of order 1 from time $t$.