{
  "id": "1306.5917",
  "version": "v4",
  "published": "2013-06-25T11:07:42.000Z",
  "updated": "2015-09-16T15:49:55.000Z",
  "title": "Upper bounds on the non-random fluctuations in first passage percolation with low moment conditions",
  "authors": [
    "Naoki Kubota"
  ],
  "comment": "This is the corrected version of the paper. 11 pages, title changed",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider first passage percolation with i.i.d. weights on edges of the d-dimensional cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the d-dimensional cubic lattice, and has moments bigger than 1, we investigate upper bounds on the so-called non-random fluctuations of the model. In addition, we give an application of our result to a lower bound for variance of the first passage percolation in the case where the limit shape has flat edges.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-05T14:00:13.000Z",
      "title": "Rates of convergence in first passage percolation with low moment conditions",
      "abstract": "We consider the first passage percolation with i.i.d.\\,weights on edges of a cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in a cubic lattice, and has a low moment, we investigate rates of convergence in first passage time. In addition, we give an application of our result to variance of the first passage percolation in the case where the limit shape has flat edges.",
      "comment": "This is the corrected version of the paper. 13 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-09-16T15:49:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F10"
    ],
    "keywords": [
      "first passage percolation",
      "low moment conditions",
      "convergence",
      "cubic lattice",
      "first passage time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5917K"
    }
  }
}