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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLabbé, Cyril
HAL ID: 9675
dc.date.accessioned2019-10-12T09:50:38Z
dc.date.available2019-10-12T09:50:38Z
dc.date.issued2019
dc.identifier.issn0022-1236
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20103
dc.language.isoenen
dc.subjectAnderson hamiltonianen
dc.subjectRegularity structuresen
dc.subjectWhite noiseen
dc.subjectSchrödinger operatoren
dc.subject.ddc519en
dc.titleThe continuous Anderson hamiltonian in d≤3en
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe construct the continuous Anderson hamiltonian on (−L,L)d driven by a white noise and endowed with either Dirichlet or periodic boundary conditions. Our construction holds in any dimension d≤3 and relies on the theory of regularity structures: it yields a self-adjoint operator in L2((−L,L)d) with pure point spectrum. In d≥2, a renormalisation of the operator by means of infinite constants is required to compensate for ill-defined products involving functionals of the white noise. We also obtain left tail estimates on the distributions of the eigenvalues: in particular, for d=3 these estimates show that the eigenvalues do not have exponential moments.en
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol277en
dc.relation.isversionofjnlissue9en
dc.relation.isversionofjnldate2019-11
dc.relation.isversionofjnlpages3187-3235en
dc.relation.isversionofdoi10.1016/j.jfa.2019.05.027en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-10-12T09:47:30Z
hal.author.functionaut


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