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arXiv · 2302.05208

Covariance inequalities for convex and log-concave functions

Michel Bonnefont·Erwan Hillion·Adrien Saumard
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Abstract

Extending results of Harg{\'e} and Hu for the Gaussian measure, we prove inequalities for the covariance Cov$_\mu(f, g)$ where $\mu$ is a general product probability measure on $\mathbb{R}^d$ and $f,g: \mathbb{R}^d \to \mathbb{R}$ satisfy some convexity or log-concavity assumptions, with possibly some symmetries.

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Michel Bonnefont, Erwan Hillion, Adrien Saumard. 2023-02-10. Covariance inequalities for convex and log-concave functions. https://arxiv.org/abs/2302.05208

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