The Borell-Ehrhard Game

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.

23 pages

References in corpus (2)

• On some inequalities for Gaussian measures
• Bellman partial differential equation and the hill property for classical isoperimetric problems

Cited by in corpus (3)

• The equality cases of the Ehrhard-Borell inequality
• Deviation inequalities for convex functions motivated by the Talagrand conjecture
• Improving constant in end-point Poincaré inequality on Hamming cube