Hydrodynamic limit for the interface model with non convex interaction

We discuss the hydrodynamic limit for the Ginzburg-Landau interface model. Under the assumption that the microscopic interaction is strictly convex, the study of the asymptotic behavior for the stochastic dynamics, including the hydrodynamic limit, is highly developed. The aim of this talk is to discuss the behavior of the interface model without the assumption of strict convexity of the potential, and to derive the hydrodynamic limit. Our analysis is based on a recent paper with Codina Cotar where the unicity of the extremal gradient Gibbs measure and the strict convexity of the surface tension is shown in the high temperature regime.

This is a joint work with T. Nishikawa and Y. Vignaud.