Spectral Moments of Random Matrices with a Rank-One Pattern of Variances

Let $\mathbf{a}_{ij}$, $1\leq i\leq j\leq n$, be independent random variables and $\mathbf{a}_{ji}=\mathbf{a}_{ij}$, for all $i,j$. Suppose that every $\mathbf{a}_{ij}$ is bounded, has zero mean, and its variance is given by $\sigma_{i}\sigma_{j}$, for a given sequence of positive real numbers $\Psi=\{\sigma_{i} , i\in\mathbb{N}\}$. Hen...More