Extremal statistics: the rightmost particle and Bramson correction
Branching Brownian motion (BBM): particles diffuse and branch at rate β. The maximum position m(t) satisfies m(t) = √(2β)·t − (3/2√(2β))·log(t) + O(1) (Bramson 1978, McKean 1975). The O(log t) correction comes from FKPP traveling waves. The extremal process (positions near max) converges to a decorated Poisson point process with Gumbel intensity.