Survival of Branching Random Walks in Random Environment

Nina Gantert (), Sebastian Müller (), Serguei Popov () and Marina Vachkovskaia ()
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Nina Gantert: CeNos Center for Nonlinear Science and Institut für Mathematische Statistik
Sebastian Müller: Technische Universität Graz
Serguei Popov: University of Campinas—UNICAMP
Marina Vachkovskaia: University of Campinas—UNICAMP

Journal of Theoretical Probability, 2010, vol. 23, issue 4, 1002-1014

Abstract: Abstract We study survival of nearest-neighbor branching random walks in random environment (BRWRE) on 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. 2×2 random matrices.

Keywords: Local extinction; Global extinction; Random matrices; Lyapunov exponent; 60K37; 60J05; 60J80 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-009-0227-5

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