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Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry
2.	Creator	Author's name, affiliation, country	Patrick Cattiaux; Université de Toulouse; France
2.	Creator	Author's name, affiliation, country	Nathael Gozlan; Université Paris-Est Marne-la-Vallée; France
2.	Creator	Author's name, affiliation, country	Arnaud Guillin; Université Blaise Pascal; France
2.	Creator	Author's name, affiliation, country	Cyril Roberto; Université Paris-Est Marne-la-Vallée; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	weighted Poincaré inequalities, weighted Cheeger inequalities, Lyapunov function, weak inequalities, isoperimetric profile
3.	Subject	Subject classification	60E15 - 26D10
4.	Description	Abstract	This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincaré and weak Cheeger, weighted Poincaré and weighted Cheeger inequalities and their dual forms. Proofs are short and we cover very large situations. For product measures on $\mathbb{R}^n$ we obtain the optimal dimension dependence using the mass transportation method. Then we derive (optimal) isoperimetric inequalities. Finally we deal with spherically symmetric measures. We recover and improve many previous result
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-04-09
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/754
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-754
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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