1. CMB 2013 (vol 57 pp. 585)
|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