Royen's proof of the Gaussian correlation inequality

Rafał Latała, Dariusz Matlak

Published 2015-12-29Version 1

We present in detail Thomas Royen's proof of the Gaussian correlation inequality which states that $\mu(K\cap L)\geq \mu(K)\mu(L)$ for any centered Gaussian measure $\mu$ on $R^d$ and symmetric convex sets $K,L$ in $R^d$.