Open Access
2016 Convergence to the stochastic Burgers equation from a degenerate microscopic dynamics
Oriane Blondel, Patrícia Gonçalves, Marielle Simon
Electron. J. Probab. 21: 1-25 (2016). DOI: 10.1214/16-EJP15


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 [7]. 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.


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Oriane Blondel. Patrícia Gonçalves. Marielle Simon. "Convergence to the stochastic Burgers equation from a degenerate microscopic dynamics." Electron. J. Probab. 21 1 - 25, 2016.


Received: 30 March 2016; Accepted: 12 November 2016; Published: 2016
First available in Project Euclid: 1 December 2016

zbMATH: 1354.60114
MathSciNet: MR3580035
Digital Object Identifier: 10.1214/16-EJP15

Primary: 35R60 , 60F17 , 60G60 , 60K35

Keywords: Degenerate rates , density fluctuations , microscopic model , porous medium equation , Stochastic Burgers equation , weak KPZ universality

Vol.21 • 2016
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