Functional inequalities for heavy tails distributions and application to isoperimetry

Details Functional inequalities for heavy tails distributions and application to isoperimetry Functional inequalities for heavy tails distributions and application to isoperimetry

2008-07-19

arxiv.org/abs/0807.3112v1

Electronic Journal of Probability (2010) 364-385

Mathematics

Probability

Scientific paper

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 Poincar\'e and weak Cheeger, weighted Poincar\'e and weighted Cheeger inequalities and their dual forms. Proofs are short and we cover very large situations. For product measures on $\R^n$ 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 results.

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