Show simple item record

dc.contributor.authorCarrapatoso, Kleber
dc.date.accessioned2012-05-16T14:30:35Z
dc.date.available2012-05-16T14:30:35Z
dc.date.issued2015
dc.identifier.issn0246-0203
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9248
dc.language.isoenen
dc.subjectmean-field limit
dc.subject.ddc519en
dc.titleQuantitative and qualitative Kac's chaos on the Boltzmann's sphere
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe investigate the construction of chaotic probability measures on the Boltzmann's sphere, which is the state space of the stochastic process of a many-particle system undergoing a dynamics preserving energy and momentum. Firstly, based on a version of the local Central Limit Theorem (or Berry-Essenn theorem), we construct a sequence of probabilities that is Kac chaotic and we prove a quantitative rate of convergence. Then, we investigate a stronger notion of chaos, namely entropic chaos introduced in \cite{CCLLV}, and we prove, with quantitative rate, that this same sequence is also entropically chaotic. Furthermore, we investigate more general class of probability measures on the Boltzmann's sphere. Using the HWI inequality we prove that a Kac chaotic probability with bounded Fisher's information is entropically chaotic and we give a quantitative rate. We also link different notions of chaos, proving that Fisher's information chaos, introduced in \cite{HaurayMischler}, is stronger than entropic chaos, which is stronger than Kac's chaos. We give a possible answer to \cite[Open Problem 11]{CCLLV} in the Boltzmann's sphere's framework. Finally, applying our previous results to the recent results on propagation of chaos for the Boltzmann equation \cite{MMchaos}, we prove a quantitative rate for the propagation of entropic chaos for the Boltzmann equation with Maxwellian molecules.
dc.relation.isversionofjnlnameAnnales de l'I.H.P. Probabilités et Statistiques
dc.relation.isversionofjnlvol51
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages993-1039
dc.relation.isversionofdoi10.1214/14-AIHP612
dc.identifier.urlsitehttps://arxiv.org/abs/1205.1241v3
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherGauthier-Villars
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingoui
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-03-10T14:25:23Z


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