5 problems

Consider perturbed simply attractive potentials, including anisotropic potentials, meaning potentials that are not necessarily isotropic. Let the variational principle be the relat…

Assume $d\geq3$ and $m=1$. A rough phase is a phase with the rough, fluctuation-dominated behavior considered in the source. No-rough-phase conjecture. There are no rough phases fo…

Assume $m=1$ and $d=2$, and consider a general simply attractive model in a rough phase. In the reference examples, suitably rescaled height functions have a scaling limit given by…

Assume $m=1$, $d=2$, and that $\Phi$ is a general discrete simply attractive potential. Let $\sigma$ denote the surface tension, and let the slopes in the dual of $\mathcal L$ be t…

Surface-tension Hessian conjecture. In the large $\beta$ and small tilt $u$ regime, the covariance matrix of the scaling limit is