TL;DR
This paper reveals that Gaussian measure convexity properties, described by Ehrhard and Borell's inequalities, can be understood through a game-theoretic minimax principle involving Brownian motion, leading to new inequalities.
Contribution
It introduces a game-theoretic framework for Gaussian convexity inequalities, providing a novel interpretation and deriving an improved reverse Brascamp-Lieb inequality.
Findings
Gaussian convexity inequalities are manifestations of a minimax game.
A new variational principle for Brownian motion is established.
An improved Gaussian version of Barthe's reverse Brascamp-Lieb inequality is obtained.
Abstract
A precise description of the convexity of Gaussian measures is provided by sharp Brunn-Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe's reverse Brascamp-Lieb inequality.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.