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


 
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1. Title Title of document Concentration inequalities for s-concave measures of dilations of Borel sets and applications
 
2. Creator Author's name, affiliation, country Matthieu Fradelizi; Université Paris-Est
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) dilation; localization lemma; Remez type inequalities; log-concave measures; large deviations; small deviations; Khintchine type inequalities; sublevel sets
 
3. Subject Subject classification 46B07; 46B09; 60B11; 52A20; 26D05
 
4. Description 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
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-09-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/695
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-695
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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