Interface Fluctuations in Non Equilibrium Stationary States: The SOS Approximation

We study the 2d stationary fluctuations of the interface in the SOS approximation of the non equilibrium stationary state found in De Masi et al. (J Stat Phys 175:203–221, 2019). We prove that the interface fluctuations are of order $N^{1/4}$, N the size of the system. We also prove that the scaling limit is a stationary Ornstein–Uhlenbeck process.