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arXiv · 2501.11018

Gaussian Correlation via Inverse Brascamp-Lieb

Emanuel Milman
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Abstract

We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this inverse inequality is in a certain sense a dual counterpart to the forward inequality of Bennett-Carbery-Christ-Tao and Valdimarsson, and that the log-concavity assumption therein cannot be omitted in general.

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Emanuel Milman. 2025-01-19. Gaussian Correlation via Inverse Brascamp-Lieb. https://arxiv.org/abs/2501.11018

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