2 problems

For $\alpha\in[0,1]$, let $f_{\mathrm{null}}(\alpha)$ be the quenched free energy of the null Random Subsequence Model, let $f^{\mathrm{BMM}}(\alpha)$ be the quenched free energy o…

Let $f_{\mathrm{pl}}(\alpha)$ and $f_{\mathrm{pl}}^{\mathrm{ann}}(\alpha)$ denote the planted quenched and annealed free energies, respectively, for aspect ratio $\alpha$. Planted…