Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems

Joseph Lehec (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Mathématiques [math]

Joseph Lehec. Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems. Bulletin canadien de mathématiques, 2014, 57, pp.585 - 597. ⟨10.4153/CMB-2013-040-x⟩. ⟨hal-01100925⟩