5 problems

Let $\phi$ be a Gaussian free field on $\mathbb{Z}^3$, and let $T_{\mathrm{rec}}^-(\mathbb{Z}^3)$ denote the lower reconstruction threshold for the three-dimensional statistical re…

Let $T_{\mathrm{rec}}^+$ denote the upper reconstruction threshold for the statistical reconstruction problem considered in the paper. Upper-threshold conjecture. … The conjecture…

Let $\phi_n$ be a zero-boundary discrete Gaussian free field converging to a continuum Gaussian free field $\Phi$, and let $\mathbb{A}_{-\lambda,\lambda}$ denote the continuum ALE.…

Let $T_{\mathrm{rec}}^-$ denote the lower reconstruction threshold for the statistical reconstruction problem considered in the paper. Lower-threshold conjecture. … The claim is pr…

Let $\beta>0$ be the inverse temperature, let \boldsymbol{\theta}=(\theta_x)_{x\in\\{-n,\ldots,n\}^2} denote Villain spins, and let $\beta'$ satisfy…