A proof of the strong Gaussian product inequality conjecture

Frédéric Ouimet, Dylan Greaves

Let $\mathbf{X}=(X_1,\dots ,X_n)$ be a centered Gaussian vector, not necessarily nondegenerate. It is proved that, for every ${\alpha }_1,\dots ,{\alpha }_n>0$, \[ \mathsf{E}\left[\prod_{i…