Scaling limit and ageing for branching random walk in Pareto environment

Marcel Ortgiese; Matthew Roberts

doi:10.1214/17-AIHP839

Scaling limit and ageing for branching random walk in Pareto environment

Marcel Ortgiese, Matthew Roberts

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

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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 language	English
Pages (from-to)	1291-1313
Number of pages	23
Journal	Annales de l'Institut Henri Poincaré: Probabilités et Statistiques
Volume	54
Issue number	3
DOIs	https://doi.org/10.1214/17-AIHP839
Publication status	Published - 11 Jul 2018

Keywords

Branching random walk
Intermittency
Parabolic Anderson model
Random environment

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/17-AIHP839

AIHP839Final published version, 258 KB

https://arxiv.org/abs/1602.08997

Cite this

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KW - Intermittency

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KW - Random environment

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Scaling limit and ageing for branching random walk in Pareto environment

Abstract

Keywords

ASJC Scopus subject areas

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EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts

Matthew Roberts

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Scaling limit and ageing for branching random walk in Pareto environment

Abstract

Keywords

ASJC Scopus subject areas

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Fingerprint

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EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts

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Matthew Roberts

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