Consider $A$, a random binary matrix of zeros and ones in $\mathbb{R}^{{M\times N}}$, and $M>N$. We assume that $P(a_{i,j}=0)=P(a_{i,j}=1)=0.5$ (although I appreciate any advice on the case of non-even probabilities). Are there any results that provide a lower bound (and maybe an interesting upper bound) on the eigenvalues of $A^TA$? The reference ring is certainly $\mathbb{R}$.

Thanks in advance!