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

We prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in the Euclidean space by a s-concave probability measure. Our result gives a common generalization of an inequality of Nazarov, Sodin and Volberg and a concentration inequality of Guedon. Applying our inequa...

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Bibliographic Details
Published inElectronic journal of probability Vol. 14; no. none; pp. 2068 - 2090
Main Author Fradelizi, Matthieu
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics (IMS) 01.01.2009
Subjects
Mathematical Physics
Mathematics
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Summary:We prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in the Euclidean space by a s-concave probability measure. Our result gives a common generalization of an inequality of Nazarov, Sodin and Volberg and a concentration inequality of Guedon. 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 measure.
ISSN:1083-6489
1083-6489
DOI:10.1214/EJP.v14-695