{
  "id": "1804.09533",
  "version": "v1",
  "published": "2018-04-25T13:09:53.000Z",
  "updated": "2018-04-25T13:09:53.000Z",
  "title": "Divergence of non-random fluctuation in First Passage Percolation",
  "authors": [
    "Shuta Nakajima"
  ],
  "comment": "9 page, 2 figures, an early version of these results appeared in Sections 1.2 and 7 of arXiv:1706.03493",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study non-random fluctuation in the first passage percolation on $\\mathbb{Z}^d$ and show that it diverges for any dimension. We also prove the divergence of the non-random shape fluctuation, which was conjectured in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation. {\\em Probab. Theory. Related. Fields.} 136(2) 298--320, 2006].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T13:09:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first passage percolation",
      "divergence",
      "non-random shape fluctuation",
      "study non-random fluctuation",
      "yu zhang"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}