The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile

W. Hachem, P. Loubaton, J. Najim

Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^n)$ where the entries are given by $Y_{ij}^n=\frac{\sigma (i/N,j/n)}{\sqrt{n}}{X}_{ij}^n$, the $X_{ij}^n$ being centered i.i.d. a…