Electronic Journal of Probability

One-point localization for branching random walk in Pareto environment

Marcel Ortgiese and Matthew I. Roberts

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We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is concentrated in a single site with high potential. The analogous one-point localization is already known for the parabolic Anderson model, which describes the expected number of particles in the same system. In our case, we rely on very fine estimates for the behaviour of particles near a good point. This complements our earlier results that in the rescaled picture most of the mass is concentrated on a small island.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 6, 20 pp.

Received: 29 April 2016
Accepted: 22 December 2016
First available in Project Euclid: 17 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

branching random walk random environment parabolic Anderson intermittency localization

Creative Commons Attribution 4.0 International License.


Ortgiese, Marcel; Roberts, Matthew I. One-point localization for branching random walk in Pareto environment. Electron. J. Probab. 22 (2017), paper no. 6, 20 pp. doi:10.1214/16-EJP22. https://projecteuclid.org/euclid.ejp/1484622023

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