Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2295 | |
dc.contributor.author | Biskup, Marek | |
dc.contributor.author | König, Wolfgang | |
dc.contributor.author | Santos, Renato Soares dos | |
dc.date.accessioned | 2016-12-14T22:47:01Z | |
dc.date.available | 2019-06-28T08:13:58Z | |
dc.date.issued | 2016 | |
dc.description.abstract | We study the solutions to the Cauchy problem on the with random potential and localised initial data. Here we consider the random Schrödinger operator, i.e., the Laplace operator with random field, whose upper tails are doubly exponentially distributed in our case. We prove that, for large times and with large probability, a majority of the total mass of the solution resides in a bounded neighborhood of a site that achieves an optimal compromise between the local Dirichlet eigenvalue of the Anderson Hamiltonian and the distance to the origin. The processes of mass concentration and the rescaled total mass are shown to converge in distribution under suitable scaling of space and time. Aging results are also established. The proof uses the characterization of eigenvalue order statistics for the random Schrödinger operator in large sets recently proved by the first two authors. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2622 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2953 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | heat equation with random coefficients | eng |
dc.subject.other | random Schrödinger operator | eng |
dc.subject.other | Feynman-Kac formula | eng |
dc.subject.other | Anderson localisation | eng |
dc.subject.other | mass concentration | eng |
dc.subject.other | spectral expansion | eng |
dc.subject.other | eigenvalue order statistics | eng |
dc.title | Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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