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About Kac's Program in Kinetic Theory

dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorMischler, Stéphane
dc.date.accessioned2011-11-16T15:50:40Z
dc.date.available2011-11-16T15:50:40Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7531
dc.language.isoenen
dc.subjectpropagation of chaosen
dc.subjectmean-field limiten
dc.subjectBoltzmann equationen
dc.subjectjump processen
dc.subjectrelaxationen
dc.subjectKacen
dc.subject.ddc519en
dc.titleAbout Kac's Program in Kinetic Theoryen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDPMMS/CMS University of Cambridge;Royaume-Uni
dc.description.abstractenIn this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle stochastic process (now denoted as Kac's master equation) which, for chaotic data, converges to the spatially homogeneous Boltzmann equation. We answer the three following questions raised in \cite{kac}: (1) prove the propagation of chaos for realistic microscopic interactions (i.e. in our results: hard spheres and true Maxwell molecules); (2) relate the time scales of relaxation of the stochastic process and of the limit equation by obtaining rates independent of the number of particles; (3) prove the convergence of the many-particle entropy towards the Boltzmann entropy of the solution to the limit equation (microscopic justification of the $H$-theorem of Boltzmann in this context). These results crucially rely on a new theory of quantitative uniform in time estimates of propagation of chaos.en
dc.relation.isversionofjnlnameComptes rendus mathématique
dc.relation.isversionofjnlvol349
dc.relation.isversionofjnlissue23-24
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages1245-1250
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.crma.2011.11.012
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00641197/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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