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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 71 open journal systems 


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

Matthieu Fradelizi, Université Paris-Est


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 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


Full text: PDF

Pages: 2068-2090

Published on: September 28, 2009
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Electronic Journal of Probability. ISSN: 1083-6489