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arXiv · 1806.05577

An extremal property of the normal distribution, with a discrete analog

Erwan Hillion·Oliver Johnson·Adrien Saumard
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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.

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Erwan Hillion, Oliver Johnson, Adrien Saumard. 2018-06-14. An extremal property of the normal distribution, with a discrete analog. https://doi.org/10.1016/j.spl.2018.08.018

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