{
  "id": "2008.07844",
  "version": "v1",
  "published": "2020-08-18T10:44:03.000Z",
  "updated": "2020-08-18T10:44:03.000Z",
  "title": "Universality of the geodesic tree in last passage percolation",
  "authors": [
    "Ofer Busani",
    "Patrik Ferrari"
  ],
  "comment": "39 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder of width $o(N^{2/3})$ and length $o(N)$ agrees in the cylinder, with the stationary geodesic sharing the same end point. In the case of the point-to-point model, we consider width $\\delta N^{2/3}$ and length up to $\\delta^{3/2} N/(\\log(\\delta^{-1}))^3$ and provide lower and upper bound for the probability that the geodesics agree in that cylinder.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-18T10:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37"
    ],
    "keywords": [
      "geodesic tree",
      "passage percolation",
      "universality",
      "large class",
      "initial conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}