Show simple item record

dc.contributor.authorMischler, Stéphane
dc.contributor.authorHauray, Maxime
HAL ID: 8012
dc.date.accessioned2012-03-28T14:48:21Z
dc.date.available2012-03-28T14:48:21Z
dc.date.issued2014
dc.identifier.issn0022-1236
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/8607
dc.language.isoenen
dc.subjectQuantitative chaos
dc.subject.ddc515en
dc.titleOn Kac's chaos and related problems
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire d'Analyse, Topologie, Probabilités (LATP) http://www.latp.univ-mrs.fr CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III;France
dc.description.abstractenThis paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac [41] in his study of mean-field limit for systems of N undistinguishable particles as N→∞N→∞. First, we quantitatively liken three usual measures of Kac's chaos, some involving all the N variables, others involving a finite fixed number of variables. Next, we define the notion of entropy chaos and Fisher information chaos in a similar way as defined by Carlen et al. [17]. We show that Fisher information chaos is stronger than entropy chaos, which in turn is stronger than Kac's chaos. We also establish that Kac's chaos plus Fisher information bound implies entropy chaos. We then extend our analysis to the framework of probability measures with support on the Kac's spheres, revisiting [17] and giving a possible answer to [17, Open problem 11]. Last, we consider the context of probability measures mixtures introduced by De Finetti, Hewitt and Savage. We define the (level 3) Fisher information for mixtures and prove that it is l.s.c. and affine, as that was done in [64] for the level 3 Boltzmann's entropy.
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol266
dc.relation.isversionofjnlissue10
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages6055-6157
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jfa.2014.02.030
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-11-26T11:52:56Z


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record