The Borell-Ehrhard game

• 成果类型: Article
• 署名作者: van Handel, Ramon
• 署名单位: Princeton University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0762-4
• 发表日期: 2018
• 页码: 555-585
• 关键词: brascamp-lieb; REPRESENTATION; inequalities; EXISTENCE

摘要

A precise description of the convexity of Gaussian measures is provided by sharp Brunn-Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe's reverse Brascamp-Lieb inequality.