Intermittency for branching random walk in Pareto environment

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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.
Original languageEnglish
Pages (from-to)2198-2263
Number of pages66
JournalAnnals of Probability
Volume44
Issue number3
Early online date16 May 2016
DOIs
Publication statusPublished - 31 May 2016

Keywords

  • Branching random walk
  • random environment
  • Parabolic Anderson model
  • Intermittency

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