Mathematical models of critical phenomena: Emergence of interfaces

Interfaces separating two phases (e.g. water and ice) are created in  phase coexistence situations such as at 0 degree Celsius. There are different mathematical models to decribe the emergence of interfaces. We will focus here on stochastic interface models.   

Random interface models are stochastic models which aim at explaining the macroscopic shape of an interface given the microscopic interaction of its particles (e.g. molecules). In this talk we would like to explain how general  Gaussian interface models emerge from scaling limits of some observable of the sandpiles models (aka avalanche model or chip-firering game).

The results presented in this talk are in collaboration with A. Cipriani (UC London), L. Chiarini (UU), J. de Graaff (TU Delft), R. Hazra (U Leiden) and M. Jara (IMPA).