Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry

@article{Cattiaux2008FunctionalIF,
  title={Functional Inequalities for Heavy Tailed Distributions and Application to Isoperimetry},
  author={Patrick Cattiaux and Nathael Gozlan and Arnaud Guillin and Cyril Roberto},
  journal={Electronic Journal of Probability},
  year={2008},
  volume={15},
  pages={346-385}
}
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 Poincare and weak Cheeger, weighted Poincare 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… 

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