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.
Publié le : 2007-01-14
Classification:
Shape theorem,
recurrence,
transience,
subadditive ergodic theorem,
nestling,
hitting time,
60K37,
60J80,
82D30
@article{1174324124,
author = {Comets, Francis and Popov, Serguei},
title = {On multidimensional branching random walks in random environment},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 68-114},
language = {en},
url = {http://dml.mathdoc.fr/item/1174324124}
}
Comets, Francis; Popov, Serguei. On multidimensional branching random walks in random environment. Ann. Probab., Tome 35 (2007) no. 1, pp. 68-114. http://gdmltest.u-ga.fr/item/1174324124/