Open Access
January 2007 On multidimensional branching random walks in random environment
Francis Comets, Serguei Popov
Ann. Probab. 35(1): 68-114 (January 2007). DOI: 10.1214/009117906000000926


We study branching random walks in random i.i.d. environment in ℤd, d≥1. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of lattice sites which are visited up to a large time.


Download Citation

Francis Comets. Serguei Popov. "On multidimensional branching random walks in random environment." Ann. Probab. 35 (1) 68 - 114, January 2007.


Published: January 2007
First available in Project Euclid: 19 March 2007

zbMATH: 1114.60084
MathSciNet: MR2303944
Digital Object Identifier: 10.1214/009117906000000926

Primary: 60K37
Secondary: 60J80 , 82D30

Keywords: hitting time , nestling , recurrence , shape theorem , subadditive ergodic theorem , transience

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • January 2007
Back to Top