Eigenvalue order statistics for random Schrödinger operators with doubly-exponential tails

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume1873
dc.contributor.authorBiskup, Marek
dc.contributor.authorKönig, Wolfgang
dc.date.accessioned2016-03-24T17:37:48Z
dc.date.available2019-06-28T08:22:20Z
dc.date.issued2013
dc.description.abstractWe consider random Schrödinger operators of the form Delta+zeta , where D is the lattice Laplacian on Zd and Delta is an i.i.d. random field, and study the extreme order statistics of the eigenvalues for this operator restricted to large but finite subsets of Zd. We show that for sigma with a doubly-exponential type of upper tail, the upper extreme order statistics of the eigenvalues falls into the Gumbel max-order class. The corresponding eigenfunctions are exponentially localized in regions where zeta takes large, and properly arranged, values. A new and self-contained argument is thus provided for Anderson localization at the spectral edge which permits a rather explicit description of the shape of the potential and the eigenfunctions. Our study serves as an input into the analysis of an associated parabolic Anderson problem.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn0946-8633
dc.identifier.urihttps://doi.org/10.34657/2293
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/3323
dc.language.isoengeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastikeng
dc.relation.issn0946-8633eng
dc.rights.licenseThis 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.licenseDieses 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.subjectParabolic Anderson modeleng
dc.subjectrandom Schrödinger operatoreng
dc.subjecteigenvalue order statisticseng
dc.subjectPoisson point process convergenceeng
dc.subjectAnderson localisationeng
dc.subject.ddc510eng
dc.titleEigenvalue order statistics for random Schrödinger operators with doubly-exponential tailseng
dc.typereporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
775155209.pdf
Size:
326.91 KB
Format:
Adobe Portable Document Format
Description: