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arXiv · 1302.2066

Short probabilistic proof of the Brascamp-Lieb and Barthe theorems

Joseph Lehec
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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.

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Joseph Lehec. 2013-02-08. Short probabilistic proof of the Brascamp-Lieb and Barthe theorems. https://doi.org/10.4153/cmb-2013-040-x

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