Escape probabilities for branching Brownian motion among mild obstacles

Jean-Francois Le Gall, Amandine Veber

Published 2010-03-19, updated 2011-01-17Version 2

We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial differential equation with singular boundary conditions. The proofs depend on a quenched homogenization theorem for branching Brownian motion among mild obstacles.