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May 2016 Intermittency for branching random walk in Pareto environment
Marcel Ortgiese, Matthew I. Roberts
Ann. Probab. 44(3): 2198-2263 (May 2016). DOI: 10.1214/15-AOP1021

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.

Citation

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Marcel Ortgiese. Matthew I. Roberts. "Intermittency for branching random walk in Pareto environment." Ann. Probab. 44 (3) 2198 - 2263, May 2016. https://doi.org/10.1214/15-AOP1021

Information

Received: 1 May 2014; Revised: 1 February 2015; Published: May 2016
First available in Project Euclid: 16 May 2016

zbMATH: 1352.60133
MathSciNet: MR3502604
Digital Object Identifier: 10.1214/15-AOP1021

Subjects:
Primary: 60K37
Secondary: 60J80

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 3 • May 2016
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