Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics - Institut Camille Jordan Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Probability Année : 2016

Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics

Résumé

In this paper we prove the convergence to the stochastic Burgers equation from one-dimensional interacting particle systems, whose dynamics allow the degeneracy of the jump rates. To this aim, we provide a new proof of the second order Boltzmann-Gibbs principle introduced in [Gon\c{c}alves, Jara 2014]. The main technical difficulty is that our models exhibit configurations that do not evolve under the dynamics - the blocked configurations - and are locally non-ergodic. Our proof does not impose any knowledge on the spectral gap for the microscopic models. Instead, it relies on the fact that, under the equilibrium measure, the probability to find a blocked configuration in a finite box is exponentially small in the size of the box. Then, a dynamical mechanism allows to exchange particles even when the jump rate for the direct exchange is zero.

Dates et versions

hal-01295541 , version 1 (31-03-2016)

Identifiants

Citer

Oriane Blondel, Patricia Gonçalves, Marielle Simon. Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics. Electronic Journal of Probability, 2016, 21 (69), pp.25. ⟨10.1214/16-EJP15⟩. ⟨hal-01295541⟩
205 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More