The shape of the \((2+1)\)D SOS surface above a wall (Q456634)

The \((2+1)\)-dimensional solid-on-solid (SOS) model is a crystal surface model. In the paper the ensemble of all level lines of the low temperature \((2+1)\)-dimensional SOS on an \(L\times L\) box is considered and the following questions are formulated:NEWLINENEWLINE (i) Do these jointly converge to a scaling limit as \(L\to\infty\), e.g., in Hausdorff distance?NEWLINENEWLINE (ii) Can the limit be explicitly described?NEWLINENEWLINE (iii) For finite large \(L\), what are the fluctuations of the level lines around their limit?NEWLINENEWLINEIn the paper, the authors fully solve the questions (i) and (ii) and particularly answer the question (iii).