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2009 Concentration inequalities for $s$-concave measures of dilations of Borel sets and applications
Matthieu Fradelizi
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Electron. J. Probab. 14: 2068-2090 (2009). DOI: 10.1214/EJP.v14-695


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 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 measure


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Matthieu Fradelizi. "Concentration inequalities for $s$-concave measures of dilations of Borel sets and applications." Electron. J. Probab. 14 2068 - 2090, 2009.


Accepted: 28 September 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1198.46008
MathSciNet: MR2550293
Digital Object Identifier: 10.1214/EJP.v14-695

Primary: 46B07
Secondary: 26D05 , 46B09 , 52A20 , 60B11

Keywords: dilation , Khintchine type inequalities , large deviations , localization lemma , Log-concave measures , Remez type inequalities , Small deviations , sublevel sets

Vol.14 • 2009
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