turkmath.org

We study a branching Brownian motion Z evolving in Rd, where a radially decaying field of Poissonian traps is present. Each trap is a ball with constant radius. Considering a general offspring distribution and conditioning Z on non-extinction, we find the asymptotic decay rate of the annealed probability that none of the particles of Z hits a trap. The method of proof is to use a skeleton decomposition for the GaltonWatson process underlying Z and to show that the particles of finite line of descent do not contribute to the survival asymptotics. On the way, a convergence result on the conditional speed of branching Brownian motion is proved.