The Annals of Probability

Intermittency for branching random walk in Pareto environment

Marcel Ortgiese and Matthew I. Roberts

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Abstract

We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an application we show that the branching random walk is intermittent, in the sense that most particles are concentrated on one very small island with large potential. Moreover, we compare the branching random walk to the parabolic Anderson model and observe that although the two systems show similarities, the mechanisms that control the growth are fundamentally different.

Article information

Source
Ann. Probab., Volume 44, Number 3 (2016), 2198-2263.

Dates
Received: May 2014
Revised: February 2015
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1463410042

Digital Object Identifier
doi:10.1214/15-AOP1021

Mathematical Reviews number (MathSciNet)
MR3502604

Zentralblatt MATH identifier
1352.60133

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

Keywords
Branching random walk random environment parabolic Anderson model intermittency

Citation

Ortgiese, Marcel; Roberts, Matthew I. Intermittency for branching random walk in Pareto environment. Ann. Probab. 44 (2016), no. 3, 2198--2263. doi:10.1214/15-AOP1021. https://projecteuclid.org/euclid.aop/1463410042


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