Concentration inequalities for $s$-concave measures of dilations of Borel sets and applications

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dc.creatorFradelizi, Matthieu
dc.date2008-07-01
dc.date.accessioned2026-07-07T09:47:37Z
dc.date.available2026-07-07T09:47:37Z
dc.descriptionWe prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in $\mathbb{R}^n$ by a $s$-concave probability. Our result gives a common generalization of an inequality of Nazarov, Sodin and Volberg and a concentration inequality of Guédon. Applying our inequality to the level sets of functions satisfying a Remez type inequality, we deduce, as it is classical, that these functions enjoy dimension free distribution inequalities and Kahane-Khintchine type inequalities with positive and negative exponent, with respect to an arbitrary $s$-concave probability.
dc.description22 pages, submitted
dc.identifierhttps://arxiv.org/abs/0807.0080
dc.identifierhttp://arxiv.org/abs/0807.0080
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163942
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject46B07; 46B09; 60B11; 52A20; 26D05
dc.titleConcentration inequalities for $s$-concave measures of dilations of Borel sets and applications
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