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arXiv · 2111.05110

Improved log-concavity for rotationally invariant measures of symmetric convex sets

Dario Cordero-Erausquin·Liran Rotem
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Abstract

We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case of log-concave measures, for instance to Cauchy measures as well. For the proof, new sharp weighted Poincar\'e inequalities are obtained for even probability measures that are log-concave with respect to a rotationally invariant measure.

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Dario Cordero-Erausquin, Liran Rotem. 2021-11-09. Improved log-concavity for rotationally invariant measures of symmetric convex sets. https://arxiv.org/abs/2111.05110

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