Improved log-concavity for rotationally invariant measures of symmetric convex sets
Metric Geometry
2022-10-03 v3 Probability
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.
Keywords
Cite
@article{arxiv.2111.05110,
title = {Improved log-concavity for rotationally invariant measures of symmetric convex sets},
author = {Dario Cordero-Erausquin and Liran Rotem},
journal= {arXiv preprint arXiv:2111.05110},
year = {2022}
}
Comments
typos and references fixed