3 problems

Let $n_1=n_2=n$, let $\theta$ be the worst-case anti-Monge matrix constructed above, and observe $y=\theta+\varepsilon$, where the entries of $\varepsilon$ are independent and dist…

Let $n_1=n_2=n$, and let $\theta\in\mathcal{M}^{n,n}$ be the anti-Monge matrix constructed in the preceding proof, with $V(\theta)=V_0$ and with low-rank approximation error of ord…

Let $\mathbf{X}$ be a low-rank matrix observed in the matrix denoising model, let $\rho$ denote its asymptotic rank fraction, and let $\mathcal{M}(\rho\mid\mathbf{X})$ and…