The Annals of Probability
- Ann. Probab.
- Volume 44, Number 3 (2016), 2198-2263.
Intermittency for branching random walk in Pareto environment
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.
Ann. Probab., Volume 44, Number 3 (2016), 2198-2263.
Received: May 2014
Revised: February 2015
First available in Project Euclid: 16 May 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K37: Processes in random environments
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
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