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dc.contributor.authorMalrieu, Florent
dc.contributor.authorGuillin, Arnaud
dc.contributor.authorCattiaux, Patrick
dc.date.accessioned2009-07-06T14:39:27Z
dc.date.available2009-07-06T14:39:27Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/832
dc.language.isoenen
dc.subjectConcentration inequalities
dc.subjectLogarithmic Sobolev Inequalities
dc.subjecttransportation cost inequality
dc.subjectGranular media equationen
dc.subject.ddc519en
dc.titleProbabilistic approach for granular media equations in the non uniformly convex caseen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherCNRS - Université de Versailles-Saint Quentin en Yvelines - Polytechnique X;France
dc.contributor.editoruniversityotherCNRS - Université de Rennes I - Ecole Normale Supérieure de Cachan - Institut National des Sciences Appliquées de Rennes;France
dc.contributor.editoruniversityotherUniversité de Paris Ouest Nanterre La Défense;France
dc.description.abstractenWe use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. Proof is straightforward, simplifying deeply proofs of Carrillo-McCann-Villani \cite{CMV,CMV2} and completing results of Malrieu \cite{malrieu03} in the uniformly convex case. It relies on an uniform propagation of chaos property and a direct control in Wasserstein distance of solutions starting with different initial measures. The deviation inequality is obtained via a $T_1$ transportation cost inequality replacing the logarithmic Sobolev inequality which is no more clearly dimension free.en
dc.relation.isversionofjnlnameProbability Theory and Related Fields
dc.relation.isversionofjnlvol140en
dc.relation.isversionofjnlissue1-2en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages19-40en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00440-007-0056-3
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00021591/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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