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

Sebastian Müller (University Münster)


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 Condition L of Comets and Popov [3] 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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Pages: 1189-1202

Publication Date: July 31, 2008

DOI: 10.1214/EJP.v13-517


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