{
  "id": "1806.09227",
  "version": "v1",
  "published": "2018-06-24T22:43:55.000Z",
  "updated": "2018-06-24T22:43:55.000Z",
  "title": "Restricted permutations for the simple exclusion process in discrete time over graphs",
  "authors": [
    "J. Ricardo G. Mendonça"
  ],
  "comment": "A somewhat provisional manuscript, 10 pages, 3 figures. Constructive comments are welcome",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a continuous-time stochastic process, but in many situations it would be desirable to have a discrete-time version of them. There is no generally applicable formalism for exclusion processes in discrete-time. In this paper we define the symmetric simple exclusion process in discrete time over graphs by means of restricted permutations over the labels of the vertices of the graphs and describe a straightforward sequential importance sampling algorithm to simulate the process. We investigate the approach to stationarity of the process over loop-augmented Bollob\\'as-Chung \"cycle-with-matches\" graphs. In all cases the approach is algebraic with an exponent varying between $1$ and $2$ depending on the number of matches.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-24T22:43:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete time",
      "restricted permutations",
      "symmetric simple exclusion process",
      "wide range applicability",
      "straightforward sequential importance sampling algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}