Electronic Journal of Probability

Branching Random Walks in Random Environment are Diffusive in the Regular Growth Phase

Hadrian Heil, Nakashima Makoto, and Yoshida Nobuo

Full-text: Open access

Abstract

We treat branching random walks in random environment using the framework of Linear Stochastic Evolution. In spatial dimensions three or larger, we establish diusive behaviour in the entire growth phase. This can be seen through a Central Limit Theorem with respect to the population density as well as through an invariance principle for a path measure we introduce.

Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 48, 1318-1340.

Dates
Accepted: 2 August 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820217

Digital Object Identifier
doi:10.1214/EJP.v16-922

Mathematical Reviews number (MathSciNet)
MR2827461

Zentralblatt MATH identifier
1244.60100

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles 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 invariance principle di

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Heil, Hadrian; Makoto, Nakashima; Nobuo, Yoshida. Branching Random Walks in Random Environment are Diffusive in the Regular Growth Phase. Electron. J. Probab. 16 (2011), paper no. 48, 1318--1340. doi:10.1214/EJP.v16-922. https://projecteuclid.org/euclid.ejp/1464820217


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