Survival of Branching Random Walks in Random Environment

Author(s)

Gantert, Nina ^{[1, 2]} ; Mueller, Sebastian ^[3] ; Popov, Serguei ^[4] ; Vachkovskaia, Marina ^[4]

Affiliation

^[1] CeNos Ctr Nonlinear Sci, Fachbereich Math & Informat, D-48149 Munster - Germany

^[2] Inst Stat Math, D-48149 Munster - Germany

^[3] Graz Univ Technol, Inst Math Strukturtheorie, A-8010 Graz - Austria

^[4] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Dept Stat, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF THEORETICAL PROBABILITY; v. 23, n. 4, p. 1002-1014, DEC 2010.
• Web of Science Citations: 14

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. 2x2 random matrices. (AU)

• FAPESP's process: 04/07276-2 - Stochastic Modelling of Interacting Systems
• Grantee: Luiz Renato Gonçalves Fontes
• Support type: Research Projects - Thematic Grants