dc.contributor.author Eldan, Ronen dc.contributor.author Lehec, Joseph HAL ID: 11520 ORCID: 0000-0001-6182-9427 dc.date.accessioned 2015-01-13T09:02:39Z dc.date.available 2015-01-13T09:02:39Z dc.date.issued 2014 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/14512 dc.description Lecture Notes in Mathematics n°2116 dc.language.iso en en dc.subject Gaussian vector dc.subject Thin-Shell Estimates dc.subject Chaining techniques dc.subject.ddc 519 en dc.title Bounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates dc.type Chapitre d'ouvrage dc.contributor.editoruniversityother University of Washington;États-Unis dc.description.abstracten Chaining 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.city Paris en dc.identifier.citationpages 107-122 dc.relation.ispartoftitle Geometric Aspects of Functional Analysis. Israel Seminar (GAFA) 2011-2013 dc.relation.ispartofeditor Bo'az Klartag, Emanuel Milman dc.relation.ispartofpublname Springer dc.relation.ispartofpublcity Berlin Heidelberg dc.relation.ispartofdate 2014 dc.relation.ispartofurl 10.1007/978-3-319-09477-9 dc.identifier.urlsite https://arxiv.org/abs/1306.3696v2 dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.relation.ispartofisbn 978-3-319-09476-2 dc.relation.forthcoming non en dc.description.submitted non en dc.identifier.doi 10.1007/978-3-319-09477-9_9 dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.date.updated 2017-03-10T14:11:48Z
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