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arXiv · 2002.12871

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

Giovanni Pistone
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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.

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Giovanni Pistone. 2021-01-07. Information Geometry of smooth densities on the Gaussian space: Poincaré inequalities. https://arxiv.org/abs/2002.12871

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