Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume2439
dc.contributor.authorBiskup, Marek
dc.contributor.authorFukushima, Ryoki
dc.contributor.authorKönig, Wolfgang
dc.date.accessioned2017-11-14T00:49:28Z
dc.date.available2019-06-28T08:06:52Z
dc.date.issued2017
dc.description.abstractWe consider random Schrödinger operators with Dirichlet boundary conditions outside lattice approximations of a smooth Euclidean domain and study the behavior of its lowest-lying eigenvalues in the limit when the lattice spacing tends to zero. Under a suitable moment assumption on the random potential and regularity of the spatial dependence of its mean, we prove that the eigenvalues of the random operator converge to those of a deterministic Schrödinger operator. Assuming also regularity of the variance, the fluctuation of the random eigenvalues around their mean are shown to obey a multivariate central limit theorem. This extends the authors recent work where similar conclusions have been obtained for bounded random potentials.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.urihttps://doi.org/10.34657/2294
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2450
dc.language.isoengeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastikeng
dc.relation.doihttps://doi.org/10.20347/WIAS.PREPRINT.2439
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.subjectRandom Schrödinger operatoreng
dc.subjectAnderson Hamiltonianeng
dc.subjecteigenvalueeng
dc.subjectspectral statisticseng
dc.subjecthomogenizationeng
dc.subjectcentral limit theoremeng
dc.subject.ddc510eng
dc.titleEigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentialseng
dc.typereporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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