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Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems

Lehec, Joseph (2014), Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems, Bulletin canadien de mathématiques, 57, p. 585-597. http://dx.doi.org/10.4153/CMB-2013-040-x

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01100925
Date
2014
Journal name
Bulletin canadien de mathématiques
Volume
57
Publisher
Canadian Mathematical Society
Pages
585-597
Publication identifier
Metadata
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Author(s)
Lehec, Joseph cc
Abstract (EN)
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.
Subjects / Keywords
Functional inequalities; Brownian motion