How to cite item

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

   
@article{EJP695,
	author = {Matthieu Fradelizi},
	title = {Concentration inequalities for s-concave measures of dilations of Borel sets and applications},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {dilation; localization lemma; Remez type inequalities; log-concave measures; large deviations; small deviations; Khintchine type inequalities; sublevel sets},
	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},
	pages = {no. 71, 2068-2090},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-695},    
        url = {http://ejp.ejpecp.org/article/view/695}}