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|Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems|
We give a short proof of the Brascamp-Lieb theorem, which asserts that a certain general form of Young's convolution inequality is saturated by Gaussian functions. The argument is inspired by Borell's stochastic proof of the PrÃ©kopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.
Keywords:functional inequalities, Brownian motion