The Annals of Probability
- Ann. Probab.
- Volume 35, Number 1 (2007), 68-114.
On multidimensional branching random walks in random environment
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.
Ann. Probab., Volume 35, Number 1 (2007), 68-114.
First available in Project Euclid: 19 March 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K37: Processes in random environments
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
Comets, Francis; Popov, Serguei. On multidimensional branching random walks in random environment. Ann. Probab. 35 (2007), no. 1, 68--114. doi:10.1214/009117906000000926. https://projecteuclid.org/euclid.aop/1174324124