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arXiv · 2403.06615

Rigid characterizations of probability measures through independence, with applications

Thomas A. Courtade
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Abstract

Three equivalent characterizations of probability measures through independence criteria are given. These characterizations lead to a family of Brascamp--Lieb-type inequalities for relative entropy, determine equilibrium states and sharp rates of convergence for certain linear Boltzmann-type dynamics, and unify an assortment of $L^2$ inequalities in probability.

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Thomas A. Courtade. 2024-03-11. Rigid characterizations of probability measures through independence, with applications. https://arxiv.org/abs/2403.06615

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