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Article Dans Une Revue Electronic Journal of Probability Année : 2009

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

Résumé

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.

Dates et versions

hal-00693040 , version 1 (01-05-2012)

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Matthieu Fradelizi. Concentration inequalities for s-concave measures of dilations of Borel sets and applications. Electronic Journal of Probability, 2009, 14, pp.2068-2090. ⟨10.1214/EJP.v14-695⟩. ⟨hal-00693040⟩
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