An extremal property of the normal distribution, with a discrete analog
Probability
2019-05-09 v1
Abstract
We prove, using the Brascamp-Lieb inequality, that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matrix. We also give a similar characterization of the Poisson measure in the discrete case, using "Chebyshev's other inequality". We briefly discuss how these results relate to Stein and Stein-Chen methods for Gaussian and Poisson approximation, and to the Bakry-Emery calculus.
Keywords
Cite
@article{arxiv.1806.05577,
title = {An extremal property of the normal distribution, with a discrete analog},
author = {Erwan Hillion and Oliver Johnson and Adrien Saumard},
journal= {arXiv preprint arXiv:1806.05577},
year = {2019}
}
Comments
7 pages