From dimension free concentration to Poincaré inequality

2013/05/19 by Nathael Gozlan, Nathaël Gozlan, Gozlan, Nathael +4
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.1305.4331

openalex publication_date 2013/05/19 · arxiv created 2013/10/09 · arxiv updated 2013/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a probability measure on an abstract metric space satisfies a non trivial dimension free concentration inequality for the ℓ₂ metric if and only if it satisfies the Poincaré inequality.

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