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

2020/02/28 by Giovanni Pistone, Pistone, Giovanni
Biochemistry, Genetics and Molecular Biology · #Bone Metabolism and Diseases #Cancer, Lipids, and Metabolism #FOS: Mathematics #Statistics Theory (math.ST) #TGF-β signaling in diseases

paper · pdf · doi:10.48550/arxiv.2002.12871

openalex publication_date 2020/02/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We derive bounds for the Orlicz norm of the deviation of a random variable defined on ℝⁿ 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.

Related

• Variance estimates and almost Euclidean structure
• Information Geometry of the Gaussian Space
• Lower bounds on Information Divergence
• Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II
• Orlicz-space Hardy and Landau-Kolmogorov inequalities for Gaussian measures