@State the Marchenko-Pastur theorem.
Suppose:
Then the singular values of $X$ follow the Marchenko-Pastur distribution with density
\[\sigma \sim \frac 1 x \sqrt{((\sqrt m + \sqrt n) - x)(x - (\sqrt m - \sqrt n))}\]and support $[\sqrt m - \sqrt n, \sqrt m + \sqrt n]$.
The Marchenko-Pastur theorem status that if:
Then the singular values of $X$ follow the Marchenko-Pastur distribution with density
\[\sigma \sim \frac 1 x \sqrt{((\sqrt m + \sqrt n) - x)(x - (\sqrt m - \sqrt n))}\]and support $[\sqrt m - \sqrt n, \sqrt m + \sqrt n]$.
Use this to @state an estimate for the minimum and maximum singular value, and hence the condition number of a rectangular matrix.
\[\begin{aligned} &\sigma _ \min(X) \approx \sqrt m + \sqrt n \\ &\sigma _ \max(X) \approx \sqrt m - \sqrt n \\ &\kappa _ 2(X) \approx \frac{1 + \sqrt{n / m}}{1 - \sqrt{n / m}} = O(1) \end{aligned}\]and hence rectangular matrices are well-conditioned with enormous probability.