| Título: | Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry |
| Autores: |
Cattiaux, Patrick; Université de Toulouse Gozlan, Nathael; Université Paris-Est Marne-la-Vallée Guillin, Arnaud; Université Blaise Pascal Roberto, Cyril; Université Paris-Est Marne-la-Vallée |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
weighted Poincaré inequalities, weighted Cheeger inequalities, Lyapunov function, weak inequalities, isoperimetric profile 60E15 - 26D10 |
| Descripción: | 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 |
| Idioma: | No aplica |
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