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.
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https://hal.archives-ouvertes.fr/hal-01295541
Contributor : Oriane Blondel <>
Submitted on : Thursday, March 31, 2016 - 11:34:12 AM
Last modification on : Monday, May 13, 2019 - 11:20:04 AM

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

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