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dc.contributor.authorBakry, Dominique
dc.contributor.authorBolley, François
dc.contributor.authorGentil, Ivan
dc.date.accessioned2010-04-06T07:15:03Z
dc.date.available2010-04-06T07:15:03Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3815
dc.language.isoenen
dc.subjectCurvature-dimension criterionen
dc.subjectTransportation inequalityen
dc.subjectHypercontractive bounden
dc.subjectDiffusion semigroupsen
dc.subjectLogarithmic Sobolev inequalityen
dc.subject.ddc519en
dc.titleDimension dependent hypercontractivity for Gaussian kernelsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-diffusive Lévy semigroup are also investigated. Curvature-dimension criteria are the main tool in the analysis.en
dc.relation.isversionofjnlnameProbability Theory and Related Fields
dc.relation.isversionofjnlvol154
dc.relation.isversionofjnlissue3-4
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages845-874
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00440-011-0387-y
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00465879/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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