Speaker: 

Janos Englender

Institution: 

University of Colorado

Time: 

Tuesday, October 7, 2014 - 11:00am to 12:00pm

Host: 

Location: 

RH 306

We study a d-dimensional branching Brownian motion, 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 hits a trap,

asymptotically, in time. 

 

This proves to be a rich problem, motivating the proof of a general result about the speed 

of branching Brownian motion conditioned on

non-extinction. We provide an appropriate `skeleton-decomposition' for the underlying

Galton-Watson process when supercritical, and show that the `doomed particles' do 

not contribute to the asymptotic decay rate.

 

This is joint work with Mine Caglar and Mehmet Oz.