Electronic Journal of Probability
- Electron. J. Probab.
- Volume 21 (2016), paper no. 69, 25 pp.
Convergence to the stochastic Burgers equation from a degenerate microscopic dynamics
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 . 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.
Electron. J. Probab., Volume 21 (2016), paper no. 69, 25 pp.
Received: 30 March 2016
Accepted: 12 November 2016
First available in Project Euclid: 1 December 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G60: Random fields 60F17: Functional limit theorems; invariance principles 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]
Blondel, Oriane; Gonçalves, Patrícia; Simon, Marielle. Convergence to the stochastic Burgers equation from a degenerate microscopic dynamics. Electron. J. Probab. 21 (2016), paper no. 69, 25 pp. doi:10.1214/16-EJP15. https://projecteuclid.org/euclid.ejp/1480561218