{
  "id": "2011.08718",
  "version": "v1",
  "published": "2020-11-17T15:44:02.000Z",
  "updated": "2020-11-17T15:44:02.000Z",
  "title": "Cutoffs for exclusion processes on graphs with open boundaries",
  "authors": [
    "Joe P. Chen",
    "Milton Jara",
    "Rodrigo Marinho"
  ],
  "comment": "v1: 26 pages, 3 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech"
  ],
  "abstract": "We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space with Dirichlet boundary condition. Our theorem is valid on a variety of settings including, but not limited to: the $d$-dimensional grid for every integer dimension $d$; and self-similar fractal graphs and products thereof. Our method of proof is to identify a rescaled version of the density fluctuation field---the cutoff martingale---which allows us to prove the mixing time upper bound that matches the lower bound obtained via Wilson's method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-17T15:44:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K05",
      "82C22",
      "60B10",
      "60J27"
    ],
    "keywords": [
      "open boundaries",
      "density fluctuation field-the cutoff martingale-which",
      "symmetric simple exclusion processes",
      "compact metric measure space",
      "dirichlet boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}