English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The parabolic Anderson model is the Cauchy problem for the heat equation onthe integer lattice with a random potential $\xi$. We consider the case when$\{\xi(z):z\in\mathbb{Z}^d\}$ is a collection of independent identicallydistributed random variables with Weibull distribution with parameter$0<\gamma<2$, and we assume that the solution is initially localised in theorigin. We prove that, as time goes to infinity, the solution completelylocalises at just one point with high probability, and we identify theasymptotic behaviour of the localisation site. We also show that the intervalsbetween the times when the solution relocalises from one site to anotherincrease linearly over time, a phenomenon known as ageing.

Localisation and ageing in the parabolic Anderson model with Weibull potential