Short probabilistic proof of the Brascamp-Lieb and Barthe theorems

Abstract

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.

12 pages

Cited by in corpus (3)

• The Borell-Ehrhard Game
• Regularized Brascamp--Lieb inequalities
• Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality