3 problems

Let $(X_1,X_2,X_3,X_4)$ be a jointly Gaussian vector, and consider the two-dimensional vector whose components are sums of two Gaussian squares, $(X_1^2+X_2^2,X_3^2+X_4^2)$. Infini…

Drton–Xiao conjecture. The random variable

Let ${\bf Y}:=(Y_1,\ldots,Y_N)$ be an $N$-dimensional Gaussian vector with independent zero-mean components of variances $\sigma_i=E(Y_i^2)$, ordered so that…