SOS level lines and area-tilted Gibbsian line ensembles
The (2+1)D SOS model above a hard wall is a random surface studied in statistical mechanics, among other reasons, to approximate the interface in the 3D Ising model. I will discuss the problem of understanding scaling limits of the level lines of this surface, through the lens of Gibbsian line ensembles with area tilts. These are collections of non-intersecting random walks above a wall, each exponentially tilted by the area underneath it. I will describe results on scaling limits as the domain size and the number of curves grow, in two distinct regimes: the Airy line ensemble of the KPZ universality class in a special integrable case, and a different stationary infinite-volume Gibbs measure constructed by Caputo, Ioffe, and Wachtel in a non-integrable case.
This talk is partially based on joint work with Evgeni Dimitrov.