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arXiv · 0811.1748

Survival of branching random walks in random environment

Nina Gantert·Sebastian Müller·Serguei Popov·Marina Vachkovskaia
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Abstract

We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on ${\mathbb Z}$. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that local and strong local survival regimes coincide for BRWRE and that they can be characterized with the spectral radius of the first moment matrix of the process. These results are generalizations of the classification of BRWRE in recurrent and transient regimes. Our main result is a characterization of global survival that is given in terms of Lyapunov exponents of an infinite product of i.i.d. $2\times 2$ random matrices.

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Nina Gantert, Sebastian Müller, Serguei Popov, Marina Vachkovskaia. 2009-06-04. Survival of branching random walks in random environment. https://doi.org/10.1007/s10959-009-0227-5

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