IMPROVED LOG-CONCAVITY FOR ROTATIONALLY INVARIANT MEASURES OF SYMMETRIC CONVEX SETS

• 成果类型: Article
• 署名作者: Cordero-Erausquin, Dario; Rotem, Liran
• 署名单位: Sorbonne Universite; Universite Paris Cite; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1604
• 发表日期: 2023
• 页码: 987-1003
• 关键词: brunn-minkowski inequalities; Small Ball Probability; poincare

摘要

We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extend-ing 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 Poincare inequalities are obtained for even probability measures that are log-concave with respect to a rotation-ally invariant measure.