Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles

@article{Oz2015ConditionalSO,
  title={Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles},
  author={Mehmet Oz and Mine cCauglar and J'anos Englander},
  journal={arXiv: Probability},
  year={2015}
}
We study a branching Brownian motion $Z$ in $\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the whole motion when hit by a particle. Considering a general offspring distribution, we derive the decay rate of the annealed probability that none of the particles of $Z$ hits a trap, asymptotically in time $t$. This proves to be a rich problem motivating the… 
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