{
  "id": "2001.04142",
  "version": "v1",
  "published": "2020-01-13T10:32:13.000Z",
  "updated": "2020-01-13T10:32:13.000Z",
  "title": "Existence and coexistence in first-passage percolation",
  "authors": [
    "Daniel Ahlberg"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider first-passage percolation with i.i.d. non-negative weights coming from some continuous distribution under a moment condition. We review recent results in the study of geodesics in first-passage percolation and study their implications for the multi-type Richardson model. In two dimensions this establishes a dual relation between the existence of infinite geodesics and coexistence among competing types. We explain the limitations of the current techniques by presenting a partial result in dimensions higher than two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-13T10:32:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-passage percolation",
      "coexistence",
      "multi-type richardson model",
      "partial result",
      "current techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}