# Interface fluctuations in non equilibrium stationary states: the SOS approximation

## TL;DR

This paper investigates the fluctuations of a 2D interface in a non-equilibrium stationary state, demonstrating they scale as N^{1/4} and converge to a stationary Ornstein-Uhlenbeck process.

## Contribution

It provides a rigorous analysis of interface fluctuations in a non-equilibrium setting using the SOS approximation, revealing their scaling behavior and limiting process.

## Key findings

- Interface fluctuations scale as N^{1/4}
- The scaling limit is a stationary Ornstein-Uhlenbeck process
- The results are proven within the SOS approximation framework

## Abstract

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.