{
  "id": "1603.08975",
  "version": "v1",
  "published": "2016-03-29T21:39:10.000Z",
  "updated": "2016-03-29T21:39:10.000Z",
  "title": "Convergence to the Stochastic Burgers Equation from a degenerate microscopic dynamics",
  "authors": [
    "Oriane Blondel",
    "Patricia Gonçalves",
    "Marielle Simon"
  ],
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-29T21:39:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic burgers equation",
      "degenerate microscopic dynamics",
      "convergence",
      "jump rate",
      "second order boltzmann-gibbs principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160308975B"
    }
  }
}