Survival of Branching Random Walks in Random Environment

Nina Gantert, Sebastian Müller, Serguei Popov, Marina Vachkovskaia

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22 Scopus citations

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.

Original languageEnglish
Pages (from-to)1002-1014
Number of pages13
JournalJournal of Theoretical Probability
Volume23
Issue number4
DOIs
StatePublished - Dec 2010
Externally publishedYes

Keywords

  • Global extinction
  • Local extinction
  • Lyapunov exponent
  • Random matrices

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