Intermittency for branching random walk in Pareto environment

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.

Published at http://dx.doi.org/10.1214/15-AOP1021 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• A two cities theorem for the parabolic Anderson model
• Weak and almost sure limits for the parabolic Anderson model with heavy tailed potentials
• Survival and Growth of a Branching Random Walk in Random Environment

Cited by in corpus (2)

• Catalytic Branching Random Walk with Semi-exponential Increments
• A branching random walk among disasters