A CLT for Information-theoretic statistics of Gram random matrices with a given variance profile

Walid Hachem, Philippe Loubaton, Jamal Najim

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