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