---
abstract: 'We consider the weakly asymmetric simple exclusion process on the discrete space $\{1,...,n-1\}\ (n\in{{\mathbb N}})$, in contact with stochastic reservoirs, both with density $\rho\in{(0,1)}$ at the extremity points, and starting from the invariant state, namely the Bernoulli product measure of parameter $\rho$. Under time diffusive scaling $tn^2$ and for $\rho=\frac12$, when the asymmetry parameter is taken of order $1/ \sqrt n$, we prove that the density fluctuations at stationarity are macroscopically governed by the energy solution of the stochastic Burgers equation with Dirichlet boundary conditions, which is shown to be unique and different from the Cole-Hopf solution.'
address:
- 'Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal and Institut Henri Poincaré, UMS 839 (CNRS/UPMC), 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France.'
- 'Humbolt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany.'
- 'INRIA Lille Nord Europe, équipe-projet MEPHYSTO, 40 avenue du Halley, 59650 Villeneuve d’Ascq, France. '
author:
- 'Patr'' icia Gonçalves'
- Nicolas Perkowski
- Marielle Simon
bibliography:
- 'bibliography.bib'
title: Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP
---

Introduction {#s1}
