Functional inequalities for heavy tails distributions and application to isoperimetry

@misc{citeulike:3036544, 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.}, author = {Cattiaux, Patrick and Gozlan, Nathael and Guillin, Arnaud and Roberto, Cyril }, citeulike-article-id = {3036544}, eprint = {0807.3112}, keywords = {heavy-tail, inequality, probability, variational}, month = {Jul}, posted-at = {2008-07-23 10:56:07}, priority = {2}, title = {Functional inequalities for heavy tails distributions and application to isoperimetry}, url = {http://arxiv.org/abs/0807.3112}, year = {2008} }

TY - ELEC ID - citeulike:3036544 L3 - citeulike-article-id:3036544 TI - Functional inequalities for heavy tails distributions and application to isoperimetry N2 - 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. KW - heavy-tail KW - inequality KW - probability KW - variational AU - Cattiaux, Patrick AU - Gozlan, Nathael AU - Guillin, Arnaud AU - Roberto, Cyril PY - 2008/Jul/19/ UR - http://arxiv.org/abs/0807.3112 ER -