Title :

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

Author(s) :

Gonçalves, Patricia [Auteur]
Instituto Superior Técnico [IST / Técnico Lisboa]
Perkowski, Nicolas [Auteur]
Institut für Mathematik [Humboldt]
Simon, Marielle [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]

Journal title :

Annales Henri Lebesgue

Publisher :

UFR de Mathématiques - IRMAR

Publication date :

2020

ISSN :

2644-9463

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Diffusion de l'énergie dans des systèmes hamiltoniens bruitésés
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

69 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL