2 problems

Let $\boldsymbol{X}=(X_1,X_2,\dots,X_d)$ be a centered Gaussian random vector, and let $m\in\mathbb N$. Gaussian product inequality conjecture. For every $m\in\mathbb N$, one has ……

Let $X\sim\mathcal{N}_{v}(0,\Lambda)$, where $\Lambda=\operatorname{diag}(\lambda)$, and let … be the Euclidean ball of radius $\rho$. Consider the covariance matrix of the vector…