Show simple item record

dc.contributor.authorChafaï, Djalil
dc.contributor.authorHardy, Adrien
dc.contributor.authorMaïda, Mylène
dc.date.accessioned2018-01-27T16:21:09Z
dc.date.available2018-01-27T16:21:09Z
dc.date.issued2018
dc.identifier.issn0022-1236
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17362
dc.language.isoenen
dc.subjectKantorovich distance
dc.subjectConcentration of measure
dc.subjectWasserstein distance
dc.subjectTalagrand inequality
dc.subjectTransport inequality
dc.subjectTransport of measure
dc.subjectCoulomb gas
dc.subjectGinibre ensemble
dc.subjectRandom matrix
dc.subject.ddc520en
dc.titleConcentration for Coulomb gases and Coulomb transport inequalities
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the non-asymptotic behavior of Coulomb gases in dimension two and more. Such gases are modeled by an exchangeable Boltzmann-Gibbs measure with a singular two-body interaction. We obtain concentration of measure inequalities for the empirical distribution of such gases around their equilibrium measure, with respect to bounded Lipschitz and Wasserstein distances. This implies macroscopic as well as mesoscopic convergence in such distances. In particular, we improve the concentration inequalities known for the empirical spectral distribution of Ginibre random matrices. Our approach is remarkably simple and bypasses the use of renormalized energy. It crucially relies on new inequalities between probability metrics, including Coulomb transport inequalities which can be of independent interest. Our work is inspired by the one of Maïda and Maurel-Segala, itself inspired by large deviations techniques. Our approach allows to recover, extend, and simplify previous results by Rougerie and Serfaty.
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol275
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages1447-1483
dc.relation.isversionofdoi10.1016/j.jfa.2018.06.004
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01374624v2
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-07-18T14:45:11Z
hal.person.labIds60
hal.person.labIds32
hal.person.labIds32


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