%0 Journal Article
%T Fine asymptotics for the consistent maximal displacement of branching Brownian motion
%A Matthew I. Roberts
%J Mathematics
%D 2012
%I arXiv
%X It is well-known that the maximal particle in a branching Brownian motion sits near $\sqrt2 t - \frac{3}{2\sqrt2}\log t$ at time $t$. One may then ask about the paths of particles near the frontier: how close can they stay to this critical curve? Two different approaches to this question have been developed. We improve upon the best-known bounds in each case, revealing new qualitative features including marked differences between the two approaches.
%U http://arxiv.org/abs/1210.0250v4