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From Boltzmann to random matrices and beyond

dc.contributor.authorChafaï, Djalil
HAL ID: 11025
ORCID: 0000-0002-1446-1428
dc.date.accessioned2014-05-09T10:17:31Z
dc.date.available2014-05-09T10:17:31Z
dc.date.issued2015
dc.identifier.issn0240-2963
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/13273
dc.language.isoenen
dc.subjectPotential theory
dc.subjectRandom matrices
dc.subjectCircular law
dc.subjectBoltzmann
dc.subjectElectrostatics
dc.subjectCollective phenomena
dc.subjectMean-field interaction
dc.subjectCoulomb gas
dc.subjectVoiculescu
dc.subjectGinibre ensemble
dc.subjectInteracting Particle Systems
dc.subjectEntropy
dc.subjectLarge Deviations Principle
dc.subjectRiesz kernel
dc.subjectShannon
dc.subjectEquilibrium measure
dc.subjectSingular repulsion
dc.subject.ddc519en
dc.titleFrom Boltzmann to random matrices and beyond
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherInstitut Universitaire de France (IUF) http://iuf.amue.fr/ Ministère de l'Enseignement Supérieur et de la Recherche Scientifique;France
dc.description.abstractenThese expository notes propose to follow, across fields, some aspects of the concept of entropy. Starting from the work of Boltzmann in the kinetic theory of gases, various universes are visited, including Markov processes and their Helmholtz free energy, the Shannon monotonicity problem in the central limit theorem, the Voiculescu free probability theory and the free central limit theorem, random walks on regular trees, the circular law for the complex Ginibre ensemble of random matrices, and finally the asymptotic analysis of mean-field particle systems in arbitrary dimension, confined by an external field and experiencing singular pair repulsion. The text is written in an informal style driven by energy and entropy. It aims to be recreative and to provide to the curious readers entry points in the literature, and connections across boundaries.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameAnnales de la Faculté des Sciences de Toulouse
dc.relation.isversionofjnlvol24
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages641-689
dc.relation.isversionofdoi10.5802/afst.1459
dc.identifier.urlsitehttps://arxiv.org/abs/1405.1003v4
dc.relation.isversionofjnlpublisherUniversité Paul Sabatier
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2019-09-18T16:51:26Z


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