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
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