  Let $(X_{jk})_{j,k\geq 1}$ be an infinite array of i.i.d. complex random
variables, with mean 0 and variance 1. Let $\la_{n,1},...,\la_{n,n}$ be the
eigenvalues of $(\frac{1}{\sqrt{n}}X_{jk})_{1\leq j,k\leq n}$. The strong
circular law theorem states that with probability one, the empirical spectral
distribution $\frac{1}{n}(\de_{\la_{n,1}}+...+\de_{\la_{n,n}})$ converges
weakly as $n\to\infty$ to the uniform law over the unit disc
$\{z\in\dC;|z|\leq1\}$. In this short note, we provide an elementary argument
that allows to add a deterministic matrix $M$ to $(X_{jk})_{1\leq j,k\leq n}$
provided that $\mathrm{Tr}(MM^*)=O(n^2)$ and $\mathrm{rank}(M)=O(n^\al)$ with
$\al<1$. Conveniently, the argument is similar to the one used for the
non-central version of Wigner's and Marchenko-Pastur theorems.
