SPECTRAL GAP FOR SPHERICALLY SYMMETRIC LOG-CONCAVE PROBABILITY MEASURES, AND BEYOND
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BONNEFONT, Michel | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | JOULIN, Aldéric | |
| hal.structure.identifier | Beijing Normal University [BNU] | |
| dc.contributor.author | MA, Yutao | |
| dc.date.accessioned | 2024-04-04T03:22:36Z | |
| dc.date.available | 2024-04-04T03:22:36Z | |
| dc.date.created | 2014-06-17 | |
| dc.date.issued | 2016-04-01 | |
| dc.identifier.issn | 0022-1236 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194771 | |
| dc.description.abstractEn | Let $\mu$ be a probability measure on $\rr^n$ ($n \geq 2$) with Lebesgue density proportional to $e^{-V (\Vert x\Vert )}$, where $V : \rr_+ \to \rr$ is a smooth convex potential. We show that the associated spectral gap in $L^2 (\mu)$ lies between $(n-1) / \int_{\rr^n} \Vert x\Vert ^2 \mu(dx)$ and $n / \int_{\rr^n} \Vert x\Vert ^2 \mu(dx)$, improving a well-known two-sided estimate due to Bobkov. Our Markovian approach is remarkably simple and is sufficiently robust to be extended beyond the log-concave case, at the price of potentially modifying the underlying dynamics in the energy, leading to weighted Poincaré inequalities. All our results are illustrated by some classical and less classical examples. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.description.sponsorship | Géométrie des mesures convexes et discrètes - ANR-11-BS01-0007 | |
| dc.description.sponsorship | Stabilité du comportement asymptotique d'EDP, de processus stochastiques et de leurs discrétisations. - ANR-12-BS01-0019 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Log- concave probability measure | |
| dc.subject.en | Poincaré-type inequalities | |
| dc.subject.en | Diffusion operator | |
| dc.subject.en | Spectral gap | |
| dc.title.en | SPECTRAL GAP FOR SPHERICALLY SYMMETRIC LOG-CONCAVE PROBABILITY MEASURES, AND BEYOND | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1406.4621 | |
| bordeaux.journal | Journal of Functional Analysis | |
| bordeaux.volume | 270 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01009383 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01009383v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Functional%20Analysis&rft.date=2016-04-01&rft.volume=270&rft.eissn=0022-1236&rft.issn=0022-1236&rft.au=BONNEFONT,%20Michel&JOULIN,%20Ald%C3%A9ric&MA,%20Yutao&rft.genre=article |
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