The Annals of Applied Probability

Central limit theorem for branching random walks in random environment

Nobuo Yoshida

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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.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 4 (2008), 1619-1635.

Dates
First available in Project Euclid: 21 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1216677134

Digital Object Identifier
doi:10.1214/07-AAP500

Mathematical Reviews number (MathSciNet)
MR2434183

Zentralblatt MATH identifier
1145.60054

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Branching random walk random environment central limit theorem phase transition directed polymers

Citation

Yoshida, Nobuo. Central limit theorem for branching random walks in random environment. Ann. Appl. Probab. 18 (2008), no. 4, 1619--1635. doi:10.1214/07-AAP500. https://projecteuclid.org/euclid.aoap/1216677134


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