{
  "id": "2212.11561",
  "version": "v1",
  "published": "2022-12-22T09:34:33.000Z",
  "updated": "2022-12-22T09:34:33.000Z",
  "title": "Large deviations for out of equilibrium correlations in the symmetric simple exclusion process",
  "authors": [
    "Thierry Bodineau",
    "Benoit Dagallier"
  ],
  "comment": "102 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium system: the one-dimensional symmetric simple exclusion process connected with reservoirs at different densities. The Donsker-Varadhan functional encodes a variety of scales depending on the observable of interest. In this paper, we focus on the time-averaged two point correlations and investigate the large deviations from the steady state behaviour. To control two point correlations out of equilibrium, the key input is the construction of a simple approximation to the invariant measure. This approximation is quantitative in time and space as estimated through relative entropy bounds building on the work of Jara and Menezes arXiv:1810.09526.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-22T09:34:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F10",
      "82C20",
      "82C22",
      "60J27"
    ],
    "keywords": [
      "large deviations",
      "equilibrium correlations",
      "one-dimensional symmetric simple exclusion process",
      "donsker-varadhan theory",
      "point correlations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 102,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}