# Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP

3 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : We consider the weakly asymmetric simple exclusion process on the discrete space $\{1,...,n-1\}$, 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.
Type de document :
Pré-publication, Document de travail
69 pages. 2017
Domaine :

Littérature citée [46 références]

https://hal.inria.fr/hal-01626604
Contributeur : Marielle Simon <>
Soumis le : vendredi 8 décembre 2017 - 09:29:04
Dernière modification le : jeudi 11 janvier 2018 - 06:25:39

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SBE_DBC_PTRF.pdf
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### Identifiants

• HAL Id : hal-01626604, version 1
• ARXIV : 1710.11011

### Citation

Patricia Gonçalves, Nicolas Perkowski, Marielle Simon. Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP. 69 pages. 2017. 〈hal-01626604〉

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