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A note on spectral gap and weighted Poincar\'e inequalities for some one-dimensional diffusions

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBONNEFONT, Michel
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorJOULIN, Aldéric
hal.structure.identifierBeijing Normal University [BNU]
dc.contributor.authorMA, Yutao
dc.date.accessioned2024-04-04T03:20:12Z
dc.date.available2024-04-04T03:20:12Z
dc.date.issued2016-06-03
dc.identifier.issn1292-8100
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194571
dc.description.abstractEnWe present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric probability measures in dimension larger than 2. Our strategy is based on two main ingredients: on the one hand, the optimal constant in the desired weighted Poincar\'e inequality has to be rewritten as the spectral gap of a convenient Markovian diffusion operator, and on the other hand we use a recent result given by the two first authors, which allows to estimate precisely this spectral gap. In particular we are able to capture its exact value for some examples.
dc.description.sponsorshipAux frontières de l'analyse Harmonique - ANR-12-BS01-0013
dc.description.sponsorshipStabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. - ANR-12-BS01-0019
dc.description.sponsorshipGéométrie des mesures convexes et discrètes - ANR-11-BS01-0007
dc.language.isoen
dc.publisherEDP Sciences
dc.title.enA note on spectral gap and weighted Poincar\'e inequalities for some one-dimensional diffusions
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1411.5982
bordeaux.journalESAIM: Probability and Statistics
bordeaux.volume20
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01082182
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01082182v1
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