On multidimensional branching random walks in random environment

By Francis Comets, Serguei Popov. 2005

49 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/755e34146795f466229df246c86d6173d06158b7

Citations in the corpus

• The critical Branching Markov Chain is transient (2005, unknown): “not independent anymore, is considered in [4].”