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 \cite{DOP}. 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.