3 problems

SOS roughening-threshold conjecture. For every temperature satisfying $\beta^{-1}<T_r^{SOS}$, every $\varepsilon>0$, every pair of integers $m,n$, and every $a>0$,

Fix $\delta>0$ and $c>0$, and consider the probability distribution $\mathbb Q_{\beta,\delta,c,N}^{+,n}$ on $n$ ordered level-line paths $\eta_1,\ldots,\eta_n$ with weights combini…

Let $(\eta(t))_{t\geqslant 0}$ be the Glauber dynamics for the SOS model on $\Lambda=\{1,\ldots,L\}^2$ with zero boundary conditions, floor at zero and ceiling at $n^+$, and let…