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2010 Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry
Patrick Cattiaux, Nathael Gozlan, Arnaud Guillin, Cyril Roberto
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Electron. J. Probab. 15: 346-385 (2010). DOI: 10.1214/EJP.v15-754

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

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Patrick Cattiaux. Nathael Gozlan. Arnaud Guillin. Cyril Roberto. "Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry." Electron. J. Probab. 15 346 - 385, 2010. https://doi.org/10.1214/EJP.v15-754

Information

Accepted: 9 April 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1205.60039
MathSciNet: MR2609591
Digital Object Identifier: 10.1214/EJP.v15-754

Subjects:
Primary: 60E15 - 26D10

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Vol.15 • 2010
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