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

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693040
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Submitted on : Tuesday, May 1, 2012 - 7:42:45 PM
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  • HAL Id : hal-00693040, version 1

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Matthieu Fradelizi. Concentration inequalities for s-concave measures of dilations of Borel sets and applications. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2009, 14 (?), pp.2068--2090. ⟨hal-00693040⟩

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