Central limit theorem for branching random walks in random environment
Nobuo Yoshida
Source: Ann. Appl. Probab. Volume 18, Number 4 (2008), 1619-1635.
Abstract
We consider branching random walks in d-dimensional integer lattice with time–space i.i.d. offspring distributions. When d≥3 and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap. We also discuss the phase transition of this model in connection with directed polymers in random environment.
Primary Subjects: 60K37
Secondary Subjects: 60F05, 60J80, 60K35, 82D30
Keywords: Branching random walk; random environment; central limit theorem; phase transition; directed polymers
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1216677134
Digital Object Identifier: doi:10.1214/07-AAP500
Mathematical Reviews number (MathSciNet):
MR2434183
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The Annals of Applied Probability
