Rényi divergence and the central limit theorem

2016/08/05 by S. G. Bobkov, Sergey G. Bobkov, G. P. Chistyakov +5 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Inequalities and Applications #Probability (math.PR) #Statistical Mechanics and Entropy #math.PR

paper · pdf · doi:10.48550/arxiv.1608.01805

arxiv created 2016/08/05 · openalex publication_date 2016/08/05 · arxiv updated 2016/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore properties of the χ² and more general Rényi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

Cited by

• Berry-Esseen bounds for the chi-square distance in the Central Limit Theorem: a Markovian approach

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