Short probabilistic proof of the Brascamp-Lieb and Barthe theorems
Probability
2019-08-15 v1 Functional Analysis
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 Pr\'ekopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.
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Cite
@article{arxiv.1302.2066,
title = {Short probabilistic proof of the Brascamp-Lieb and Barthe theorems},
author = {Joseph Lehec},
journal= {arXiv preprint arXiv:1302.2066},
year = {2019}
}
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12 pages