Finite de Finetti bounds in relative entropy

2024/07/17 by Lampros Gavalakis, Gavalakis, Lampros, Oliver Johnson +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Inequalities and Applications #Optimization and Variational Analysis #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2407.12921

openalex publication_date 2024/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two new finite de Finetti theorems for exchangeable random vectors taking values in arbitrary spaces. These bounds are tight, and they are independent of the size and the dimension of the underlying space.

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• Symmetry-driven thermalization via finite de Finetti theorems

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