4 problems

Let $\mathbf{\mathcal S}(G,\kappa,\alpha)$ be a statistical symmetric binary perceptron, let $\alpha_{ult_s}(\kappa)$ be its $s$-level ultrametric OGP critical density, and let…

Let $\mathbf{\mathcal S}(G,\kappa,\alpha)$ be a statistical symmetric binary perceptron, let $\alpha_{ult_s}(\kappa)$ be its $s$-level ultrametric OGP critical density, let…

Let $G\nin\mathbb{R}^{m\times n}$ have independent standard-normal entries. For constraint density $\alpha=\lim_{n\to\infty}m/n$ and $\kappa\in\mathbb{R}_+$, consider the statistic…

Let $A\in\mathbb{R}^{\alpha N\times N}$ have independent standard Gaussian entries, and consider the set of $\sigma\in\{-1,+1\}^N$ satisfying $A\sigma>0$ entrywise. The largest sol…