3 problems

Let $(N_1,N_2,u,q_1,q_2)$ denote positive channel and power parameters, and let the isotropic condition mean that the maximum in the stated theorem is achieved by isotropic Gaussia…

Let $X$ be an $n$-dimensional random vector and define $X_t=X+Z_t$, where $Z_t$ is an independent Gaussian random vector with covariance matrix $tI$. Let $X_G$ be an $n$-dimensiona…

Let $X$ be an $n$-dimensional random vector, let $Z_t$ be an independent Gaussian random vector with covariance matrix $tI$, and set $X_t=X+Z_t$. Let $X_G$ be an $n$-dimensional Ga…