dc.contributor.author Mischler, Stéphane en dc.contributor.author Mouhot, Clement Mouhot en dc.date.accessioned 2018-04-23T14:37:15Z dc.date.available 2018-04-23T14:37:15Z dc.identifier.issn 1631-073X dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/275127 dc.description.abstract In 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.subject math.AP en dc.subject math.AP en dc.subject math-ph en dc.subject math.MP en dc.subject math.PR en dc.title About Kac's Program in Kinetic Theory en dc.type Article prism.endingPage 1250 prism.publicationName 2 en prism.startingPage 1245 prism.volume 4 en dc.identifier.doi 10.17863/CAM.22307 rioxxterms.versionofrecord 10.1016/j.crma.2011.11.012 en rioxxterms.version AM * rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.type Journal Article/Review en dc.identifier.url http://dx.doi.org/10.1016/j.crma.2011.11.012 en rioxxterms.freetoread.startdate 2012-12-01
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