Entropic and functional forms of the dimensional Brunn--Minkowski inequality in Gauss space

Gautam Aishwarya, Dongbin Li

Given even strongly log-concave random vectors $X_0$ and $X_1$ in ${\mathbb{R}}^n$, we show that a natural joint distribution $(X_0,X_1)$ satisfies, \begin{equation} e^{ - \f…