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Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems

Published online by Cambridge University Press:  20 November 2018

Joseph Lehec
Joseph Lehec*
Affiliation:
Ceremade (UMR CNRS 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75016 Paris, France e-mail: lehec@ceremade.dauphine.fr
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Abstract

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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 Prèkopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.

Keywords

39B6260J65functional inequalitiesBrownian motion
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 585 - 597
Copyright
Copyright © Canadian Mathematical Society 2014

References

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