Moment-entropy inequalities

• 成果类型: Article
• 署名作者: Lutwak, E; Yang, D; Zhang, GY
• 署名单位: New York University; New York University Tandon School of Engineering
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 757-774
• 关键词: dual mixed volumes; gaussian-processes; convex; bodies; tomography; VALUATIONS

摘要

It is shown that the product of the Renyi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santalo inequality).