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dc.contributor.authorMischler, Stéphaneen
dc.contributor.authorMouhot, Clement Mouhoten
dc.date.accessioned2018-04-23T14:37:15Z
dc.date.available2018-04-23T14:37:15Z
dc.identifier.issn1631-073X
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/275127
dc.description.abstractIn 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.
dc.subjectmath.APen
dc.subjectmath.APen
dc.subjectmath-phen
dc.subjectmath.MPen
dc.subjectmath.PRen
dc.titleAbout Kac's Program in Kinetic Theoryen
dc.typeArticle
prism.endingPage1250
prism.publicationName2en
prism.startingPage1245
prism.volume4en
dc.identifier.doi10.17863/CAM.22307
rioxxterms.versionofrecord10.1016/j.crma.2011.11.012en
rioxxterms.versionAM*
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.typeJournal Article/Reviewen
dc.identifier.urlhttp://dx.doi.org/10.1016/j.crma.2011.11.012en
rioxxterms.freetoread.startdate2012-12-01


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