{
  "id": "2411.13419",
  "version": "v1",
  "published": "2024-11-20T16:05:35.000Z",
  "updated": "2024-11-20T16:05:35.000Z",
  "title": "Forest Fire Model on $\\mathbb{Z}_{+}$ with Delays",
  "authors": [
    "Satyaki Bhattacharya",
    "Stanislav Volkov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a generalization of the forest fire model on $\\mathbb{Z}_+$ with ignition at zero only, studied in [arXiv:0907.1821]. Unlike that model, we allow delays in the spread of the fires as well as the non-zero burning time of individual ``trees''. We obtain some general properties for this model, which cover, among others, the phenomena of an ``infinite fire'', not present in the original model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-20T16:05:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60K35",
      "60F20"
    ],
    "keywords": [
      "general properties",
      "original model",
      "non-zero burning time",
      "individual",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}