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 Prékopa-Leindler inequality and applies also to the
reversed Brascamp-Lieb inequality, due to Barthe.
functional inequalities, Brownian motion
39B62 - Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
60J65 - Brownian motion [See also 58J65]