Gaussian Correlation via Inverse Brascamp-Lieb

• 成果类型: Article; Early Access
• 署名作者: Milman, Emanuel
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01445-x
• 发表日期: 2025-11-13
• 关键词: Gaussian correlation inequality; Inverse Brascamp-Lieb inequality; Even log-concave functions; CORRELATION-INEQUALITY; youngs-inequality; brunn-minkowski; transport; entropy

摘要

We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this inverse inequality is in a certain sense a dual counterpart to the forward inequality of Bennett-Carbery-Christ-Tao and Valdimarsson, and that the log-concavity assumption therein cannot be omitted in general.