On multidimensional branching random walks in random environment

Details On multidimensional branching random walks in random environment On multidimensional branching random walks in random environment

2005-07-06

arxiv.org/abs/math/0507126v1

Mathematics

Probability

Scientific paper

We study branching random walks in random i.i.d. environment in $\Z^d, d \geq 1$. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of lattice sites which are visited up to a large time.

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