Rigid characterizations of probability measures through independence, with applications
<|reference_start|>Rigid characterizations of probability measures through independence, with applications: 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.<|reference_end|>
@article{courtade2024rigid,
    title={Rigid characterizations of probability measures through independence,
  with applications},
    author={Thomas A. Courtade},
    journal={arXiv preprint arXiv:2403.06615},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06615},
    primaryClass={math.PR cs.IT math.IT}
}