Critical branching Brownian motion with absorption: survival probability - Berestycki, J; Berestycki, N; Schweinsberg, J (Springer Berlin Heidelberg, 2014)
We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of Mathematical expression. Kesten (Stoch Process 7:9-47, 1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time Mathematical expression. These bounds improve upon results of Kesten (Stoch Process 7:9-47, 1978), and partially confirm nonrigorous predictions of Derrida and Simon (EPL 78:60006, 2007). © 2013 Springer-Verlag Berlin Heidelberg.