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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Ehrhard inequality
- Gaussian measures
- Stochastic games