Scaling limit and ageing 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 show that the system of particles, rescaled in an appropriate way, converges in distribution to a scaling limit that is interesting in its own right. We describe the limit object as a growing collection of “lilypads” built on a Poisson point process in R d. As an application of our main theorem, we show that the maximizer of the system displays the ageing property.

Original languageEnglish
Pages (from-to)1291-1313
Number of pages23
JournalAnnales de l'Institut Henri Poincaré: Probabilités et Statistiques
Volume54
Issue number3
DOIs
Publication statusPublished - 11 Jul 2018

Fingerprint

Branching Random Walk
Scaling Limit
Pareto
Poisson Point Process
Random Potential
Branching
Converge
Theorem
Scaling
Random walk
Object
Point process

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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AB - We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show that the system of particles, rescaled in an appropriate way, converges in distribution to a scaling limit that is interesting in its own right. We describe the limit object as a growing collection of “lilypads” built on a Poisson point process in R d. As an application of our main theorem, we show that the maximizer of the system displays the ageing property.

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