Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics
Abstract
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.
Keywords
Cite
@article{arxiv.1603.08975,
title = {Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics},
author = {Oriane Blondel and Patricia Gonçalves and Marielle Simon},
journal= {arXiv preprint arXiv:1603.08975},
year = {2017}
}