# Mathematics Colloquia and Seminars

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### Branching population in random media

**Mathematical Physics & Probability**

Speaker: | Janos Englander, UC Santa Barbara |

Location: | 2112 MSB |

Start time: | Tue, May 22 2007, 2:10PM |

We study a spatial branching model, where the underlying motion is d-dimensional Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed "mild" obstacles. The main result is the quenched law of large numbers for the population for all d. We also show that the branching Brownian motion with mild obstacles spreads less quickly than ordinary branching Brownian motion by giving an upper estimate on its speed. When the underlying motion is an arbitrary diffusion process, we obtain a dichotomy for the quenched local growth that is independent of the Poissonian intensity. More general offspring distributions (beyond the dyadic one considered in the main theorems) are also discussed.