A criterion for transience of multidimensional branching random walk in random environment

Details A criterion for transience of multidimensional branching random walk in random environment A criterion for transience of multidimensional branching random walk in random environment

2007-05-14

arxiv.org/abs/0705.1874v1

Electronic Journal of Probability, 13 (2008), 1189-1202

Mathematics

Probability

Scientific paper

We develop a criterion for transience for a general model of branching Markov chains. In the case of multi-dimensional branching random walk in random environment (BRWRE) this criterion becomes explicit. In particular, we show that \emph{Condition L} of Comets and Popov is necessary and sufficient for transience as conjectured. Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp. dies out locally.

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