2 problems

Let $X_n$ be an $n\times n$ random matrix with independent and identically distributed entries having mean $0$ and variance $1/n$. Let $\rho(z)$ denote the limiting eigenvalue dens…

Let $T$ be the Toeplitz matrix, let $A_{jj}$ denote the indicated diagonal rank-one perturbation, and let $V$ denote the perturbation appearing in the source. Consider the deformat…