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.
|Number of pages||23|
|Journal||Annales de l'Institut Henri Poincaré: Probabilités et Statistiques|
|Publication status||Published - 11 Jul 2018|
- Branching random walk
- Parabolic Anderson model
- Random environment
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
FingerprintDive into the research topics of 'Scaling limit and ageing for branching random walk in Pareto environment'. Together they form a unique fingerprint.
- Department of Mathematical Sciences - Royal Society University Research Fellow & Reader
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath
Person: Research & Teaching