A Forward-Reverse Brascamp-Lieb Inequality: Entropic Duality and Gaussian Optimality

作者：Liu Jingbo; Courtade Thomas A; Cuff Paul W; Verdu Sergio

来源：Entropy, 2018, 20(6): 418.

DOI：10.3390/e20060418

• Brascamp-Lieb inequality
• hypercontractivity
• functional-entropic duality
• Gaussian optimality
• network information theory
• image size characterization

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality that unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a doubling trick used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

• 出版日期2018-6