Abstract
We consider branching random walks in d-dimensional integer lattice with time–space i.i.d. offspring distributions. When d≥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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have