Survival and Growth of a Branching Random Walk in Random Environment

Details Survival and Growth of a Branching Random Walk in Random Environment Survival and Growth of a Branching Random Walk in Random Environment

2009-06-22

arxiv.org/abs/0906.4033v2

Mathematics

Probability

Revised version, improved results. Accepted at Markov Processes and Related Fields

Scientific paper

We consider a particular Branching Random Walk in Random Environment (BRWRE) on $\sN_0$ started with one particle at the origin. Particles reproduce according to an offspring distribution (which depends on the location) and move either one step to the right (with a probability in $(0,1]$ which also depends on the location) or stay in the same place. We give criteria for local and global survival and show that global survival is equivalent to exponential growth of the moments. Further, on the event of survival the number of particles grows almost surely exponentially fast with the same growth rate as the moments.

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