Survival of Branching Random Walks in Random Environment

@article{Gantert2008SurvivalOB,
  title={Survival of Branching Random Walks in Random Environment},
  author={Nina Gantert and Sebastian M{\"u}ller and Serguei Yu. Popov and M. Vachkovskaia},
  journal={Journal of Theoretical Probability},
  year={2008},
  volume={23},
  pages={1002-1014}
}
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… 

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