The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 4 (2008), 1619-1635.
Central limit theorem for branching random walks in random environment
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.
Ann. Appl. Probab., Volume 18, Number 4 (2008), 1619-1635.
First available in Project Euclid: 21 July 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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