The low temperature SOS model above a wall and 1:2:3 scaling

Vortrag von Dr. Yujin H. Kim

Datum: 29.04.26  Zeit: 17.15 - 18.45  Raum: Y27H12

Random surfaces play a central role in probability and mathematical physics for decades. Physically, they often arise as models of interfaces: boundaries between distinct regions of space. The Solid-on-Solid (SOS) model is a canonical discrete model for interfaces separating stable (equilibrium) coexisting phases in three dimensions, such as the boundary of a solid that has crystallized in a liquid solution. In this talk, we present the fascinating geometry of the SOS model at "low temperature", conditioned to be non-negative ("above a wall": think of substration on a hard surface). In this setting, the SOS model resembles a wedding cake, being comprised of a sequence of shrinking, stacked layers whose boundaries form a collection of nested loops. Our work sheds light on the fluctuations of these loops away from their Wulff shape scaling limits, and in particular suggests a scaling limit for these fluctuations. Based on joint works with Patrizio Caddeo, Milind Hegde, Eyal Lubetzky, and Christian Serio.