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We study the infimum of the best constant in a functional inequality, theBrascamp-Lieb-like inequality, over auxiliary measures within a neighborhood ofa product distribution. In the finite alphabet and the Gaussian cases, such aninfimum converges to the best constant in a mutual information inequality.Implications for strong converse properties of two common randomness (CR)generation problems are discussed. In particular, we prove the strong converseproperty of the rate region for the omniscient helper CR generation problem inthe discrete and the Gaussian cases. The latter case is perhaps the firstinstance of a strong converse for a continuous source when the rate regioninvolves auxiliary random variables.

Smoothing Brascamp-Lieb Inequalities and Strong Converses for Common Randomness Generation