Central Limit Theorem for Branching Random Walks in Random Environment

Details Central Limit Theorem for Branching Random Walks in Random Environment Central Limit Theorem for Branching Random Walks in Random Environment

2007-12-05

arxiv.org/abs/0712.0648v1

Mathematics

Probability

15 pages

Scientific paper

We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d \ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap. We also discuss the phase transition of this model in connection with directed polymers in random environment.

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