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Functional inequalities for heavy tails distributions and application to isoperimetry | | Patrick Cattiaux
; Nathael Gozlan
; Arnaud Guillin
; Cyril Roberto
; | | Date: |
19 Jul 2008 | | 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 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. | | Source: | arXiv, 0807.3112 | | Services: | Forum | Review | PDF | Favorites | |
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