Open Access
2017 One-point localization for branching random walk in Pareto environment
Marcel Ortgiese, Matthew I. Roberts
Electron. J. Probab. 22: 1-20 (2017). DOI: 10.1214/16-EJP22


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.


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Marcel Ortgiese. Matthew I. Roberts. "One-point localization for branching random walk in Pareto environment." Electron. J. Probab. 22 1 - 20, 2017.


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

zbMATH: 1357.60093
MathSciNet: MR3613699
Digital Object Identifier: 10.1214/16-EJP22

Primary: 60K37
Secondary: 60J80

Keywords: Branching random walk , Intermittency , Localization , parabolic Anderson , random environment

Vol.22 • 2017
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