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Bounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates

dc.contributor.authorEldan, Ronen
dc.contributor.authorLehec, Joseph
HAL ID: 11520
ORCID: 0000-0001-6182-9427
dc.date.accessioned2015-01-13T09:02:39Z
dc.date.available2015-01-13T09:02:39Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14512
dc.descriptionLecture Notes in Mathematics n°2116
dc.language.isoenen
dc.subjectGaussian vector
dc.subjectThin-Shell Estimates
dc.subjectChaining techniques
dc.subject.ddc519en
dc.titleBounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates
dc.typeChapitre d'ouvrage
dc.contributor.editoruniversityotherUniversity of Washington;États-Unis
dc.description.abstractenChaining techniques show that if X is an isotropic log-concave random vector in R n and Γ is a standard Gaussian vector then EX ≤ Cn 1/4 EΓ for any norm · , where C is a universal constant. Using a completely different argument we establish a similar inequality relying on the thin-shell constant σn = sup Var(|X|); X isotropic and log-concave on R n . In particular, we show that if the thin-shell conjecture σn = O(1) holds, then n 1/4 can be replaced by log(n) in the inequality. As a consequence, we obtain certain bounds for the mean-width, the dual mean-width and the isotropic constant of an isotropic convex body. In particular, we give an alternative proof of the fact that a positive answer to the thin-shell conjecture implies a positive answer to the slicing problem, up to a logarithmic factor.
dc.publisher.cityParisen
dc.identifier.citationpages107-122
dc.relation.ispartoftitleGeometric Aspects of Functional Analysis. Israel Seminar (GAFA) 2011-2013
dc.relation.ispartofeditorBo'az Klartag, Emanuel Milman
dc.relation.ispartofpublnameSpringer
dc.relation.ispartofpublcityBerlin Heidelberg
dc.relation.ispartofdate2014
dc.relation.ispartofurl10.1007/978-3-319-09477-9
dc.identifier.urlsitehttps://arxiv.org/abs/1306.3696v2
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.ispartofisbn978-3-319-09476-2
dc.relation.forthcomingnonen
dc.description.submittednonen
dc.identifier.doi10.1007/978-3-319-09477-9_9
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-03-10T14:11:48Z


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