If $X$ denotes a $m \times n$ random matrix whose entries are independent identically distributed random variables with mean $\mu$ and $\sigma^2 < \infty$, let
$$Y = X X^T$$
with $X^T$ the transpose of $X$. Let $\lambda_1 , \lambda_2 ,\ldots, \lambda_m$ be the eigenvalues of $Y$ (viewed as random variables).
If $\mu = 0$, it is known that the law of $\lambda$ converges to Marchenko–Pastur distribution: https://en.wikipedia.org/wiki/Marchenko%E2%80%93Pastur_distribution
My question is that in the case $\mu \neq 0$ what is the limit distribution of $\lambda$?