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

ENTROPY(2018)

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摘要
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.
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关键词
Brascamp-Lieb inequality,hypercontractivity,functional-entropic duality,Gaussian optimality,network information theory,image size characterization
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