Show simple item record

dc.contributor.authorBolley, François*
dc.contributor.authorChafaï, Djalil*
dc.contributor.authorFontbona, Joaquín*
dc.date.accessioned2017-12-07T14:56:41Z
dc.date.available2017-12-07T14:56:41Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17204
dc.language.isoenen
dc.subjectCoulomb gas
dc.subjectGinibre Ensemble
dc.subjectInteracting particle system
dc.subjectPoincaré inequality
dc.subjectLyapunov function
dc.subjectMcKean-Vlasov equation
dc.subjectCox-Ingersoll-Ross process
dc.subject.ddc519en
dc.titleDynamics of a planar Coulomb gas
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the long-time behavior of the dynamics of interacting planar Brow-nian particles, confined by an external field and subject to a singular pair repulsion. The invariant law is an exchangeable Boltzmann – Gibbs measure. For a special inverse temperature, it matches the Coulomb gas known as the complex Ginibre ensemble. The difficulty comes from the interaction which is not convex, in contrast with the case of one-dimensional log-gases associated with the Dyson Brownian Motion. Despite the fact that the invariant law is neither product nor log-concave, we show that the system is well-posed for any inverse temperature and that Poincaré inequalities are available. Moreover the second moment dynamics turns out to be a nice Cox – Ingersoll – Ross process in which the dependency over the number of particles leads to identify two natural regimes related to the behavior of the noise and the speed of the dynamics.
dc.relation.isversionofjnlnameThe Annals of Applied Probability
dc.relation.isversionofjnlvol28
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages3152-3183
dc.relation.isversionofdoi10.1214/18-AAP1386
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01546288
dc.relation.isversionofjnlpublisherIMS
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-15T17:59:28Z
hal.person.labIds*
hal.person.labIds*
hal.person.labIds*


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