Branching Brownian motion with "mild" Poissonian obstacles

Details Branching Brownian motion with "mild" Poissonian obstacles Branching Brownian motion with "mild" Poissonian obstacles

2005-08-29

arxiv.org/abs/math/0508585v1

Mathematics

Probability

23 pages

Scientific paper

We study a spatial branching model, where the underlying motion is Brownian motion and the branching is affected by a random collection of reproduction blocking sets called "mild" obstacles. We show that the quenched local growth rate is given by the branching rate in the `free' region . When the underlying motion is an arbitrary diffusion process, we obtain a dichotomy for the local growth that is independent of the Poissonian intensity. Finally, and most importantly, we obtain the asymptotics (in probability) of the quenched (when $d\le 2$) and the annealed (arbitrary d) global growth rates, and identify subexponential correction terms.

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