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 language | English |
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Pages (from-to) | 1002-1014 |
Number of pages | 13 |
Journal | Journal of Theoretical Probability |
Volume | 23 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2010 |
Externally published | Yes |
Keywords
- Global extinction
- Local extinction
- Lyapunov exponent
- Random matrices