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dc.contributor.authorDumaz, Laure*
dc.contributor.authorLabbé, Cyril*
dc.date.accessioned2019-09-04T09:31:10Z
dc.date.available2019-09-04T09:31:10Z
dc.date.issued2019
dc.identifier.issn0178-8051
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19673
dc.language.isoenen
dc.subjectAnderson Hamiltonian
dc.subjectHill’s operator
dc.subjectLocalization
dc.subjectRiccati transform
dc.subjectDiffusion
dc.subject.ddc519en
dc.titleLocalization of the continuous Anderson Hamiltonian in 1-D
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the bottom of the spectrum of the Anderson Hamiltonian HL:=−∂2x+ξ on [0, L] driven by a white noise ξ and endowed with either Dirichlet or Neumann boundary conditions. We show that, as L→∞, the point process of the (appropriately shifted and rescaled) eigenvalues converges to a Poisson point process on R with intensity exdx, and that the (appropriately rescaled) eigenfunctions converge to Dirac masses located at independent and uniformly distributed points. Furthermore, we show that the shape of each eigenfunction, recentered around its maximum and properly rescaled, is given by the inverse of a hyperbolic cosine. We also show that the eigenfunctions decay exponentially from their localization centers at an explicit rate, and we obtain very precise information on the zeros and local maxima of these eigenfunctions. Finally, we show that the eigenvalues/eigenfunctions in the Dirichlet and Neumann cases are very close to each other and converge to the same limits.
dc.relation.isversionofjnlnameProbability Theory and Related Fields
dc.relation.isversionofjnlvol176
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages353–419
dc.relation.isversionofdoi10.1007/s00440-019-00920-6
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-07-01T12:42:11Z
hal.person.labIds60*
hal.person.labIds60*


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