For a random matrix $A\in\mathbb{R}^{N\times n}$ with iid entries, with mean zero, variance $\mathbb{E}[a_{11}^2]$, and bounded fourth moment, I know that when $N$ and $n$ are sufficiently large, the extreme eigenvalues of $A^TA$ concentrate around the following values \begin{align} \lambda_{\max}(A^TA)&\simeq(\sqrt{N}+\sqrt{n})^2 \mathbb{E}[a_{11}^2] ,\\ \lambda_{\min}(A^TA)&\simeq(\sqrt{N}-\sqrt{n})^2 \mathbb{E}[a_{11}^2] , \end{align}
which is a quite classic result.
Is there any variation of this result known for the case when the mean is not zero (but still iid, so all entries with the same mean) ?
