Information Geometry of smooth densities on the Gaussian space: Poincaré inequalities

Abstract

We derive bounds for the Orlicz norm of the deviation of a random variable defined on ${\mathbb{R}}^n$ from its Gaussian mean value. The random variables are assumed to be smooth and the bound itself depends on the Orlicz norm of the gradient. Applications to non-parametric Information Geometry are discussed.

arXiv commentAccepted. Minor corrections