| dc.contributor.author | Malrieu, Florent | |
| dc.contributor.author | Guillin, Arnaud | |
| dc.contributor.author | Cattiaux, Patrick | |
| dc.date.accessioned | 2009-07-06T14:39:27Z | |
| dc.date.available | 2009-07-06T14:39:27Z | |
| dc.date.issued | 2008 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/832 | |
| dc.language.iso | en | en |
| dc.subject | Concentration inequalities | |
| dc.subject | Logarithmic Sobolev Inequalities | |
| dc.subject | transportation cost inequality | |
| dc.subject | Granular media equation | en |
| dc.subject.ddc | 519 | en |
| dc.title | Probabilistic approach for granular media equations in the non uniformly convex case | en |
| dc.type | Article accepté pour publication ou publié | |
| dc.contributor.editoruniversityother | CNRS - Université de Versailles-Saint Quentin en Yvelines - Polytechnique X;France | |
| dc.contributor.editoruniversityother | CNRS - Université de Rennes I - Ecole Normale Supérieure de Cachan - Institut National des Sciences Appliquées de Rennes;France | |
| dc.contributor.editoruniversityother | Université de Paris Ouest Nanterre La Défense;France | |
| dc.description.abstracten | We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. Proof is straightforward, simplifying deeply proofs of Carrillo-McCann-Villani \cite{CMV,CMV2} and completing results of Malrieu \cite{malrieu03} in the uniformly convex case. It relies on an uniform propagation of chaos property and a direct control in Wasserstein distance of solutions starting with different initial measures. The deviation inequality is obtained via a $T_1$ transportation cost inequality replacing the logarithmic Sobolev inequality which is no more clearly dimension free. | en |
| dc.relation.isversionofjnlname | Probability Theory and Related Fields | |
| dc.relation.isversionofjnlvol | 140 | en |
| dc.relation.isversionofjnlissue | 1-2 | en |
| dc.relation.isversionofjnldate | 2008 | |
| dc.relation.isversionofjnlpages | 19-40 | en |
| dc.relation.isversionofdoi | http://dx.doi.org/10.1007/s00440-007-0056-3 | |
| dc.identifier.urlsite | http://hal.archives-ouvertes.fr/hal-00021591/en/ | en |
| dc.description.sponsorshipprivate | oui | en |
| dc.relation.isversionofjnlpublisher | Springer | |
| dc.subject.ddclabel | Probabilités et mathématiques appliquées | en |
