Electronic Journal of Probability

Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry

Patrick Cattiaux, Nathael Gozlan, Arnaud Guillin, and Cyril Roberto

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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

Article information

Electron. J. Probab., Volume 15 (2010), paper no. 13, 346-385.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E15 - 26D10

weighted Poincaré inequalities weighted Cheeger inequalities Lyapunov function weak inequalities isoperimetric profile

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Cattiaux, Patrick; Gozlan, Nathael; Guillin, Arnaud; Roberto, Cyril. Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry. Electron. J. Probab. 15 (2010), paper no. 13, 346--385. doi:10.1214/EJP.v15-754. https://projecteuclid.org/euclid.ejp/1464819798

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