{
  "id": "2001.03961",
  "version": "v1",
  "published": "2020-01-12T17:12:38.000Z",
  "updated": "2020-01-12T17:12:38.000Z",
  "title": "Local stationarity of exponential last passage percolation",
  "authors": [
    "Márton Balázs",
    "Ofer Busani",
    "Timo Seppäläinen"
  ],
  "comment": "36 pages, 8 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider point to point last passage times to every vertex in a neighbourhood of size $\\delta N^{\\frac{2}{3}}$, distance $N$ away from the starting point. The increments of these last passage times in this neighbourhood are shown to be \\emph{jointly equal} to their stationary versions with high probability that depends on $\\delta$ only. With the help of this result we show that 1) the tree of point to point geodesics starting from every vertex in a box of side length $\\delta N^{\\frac{2}{3}}$ going to a point at distance $N$ agree inside the box with the tree of infinite geodesics going in the same direction; 2) two geodesics starting from $N^{\\frac{2}{3}}$ away from each other, to a point at distance $N$ will not coalesce too close to either endpoints on the macroscopic scale.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-12T17:12:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37"
    ],
    "keywords": [
      "passage percolation",
      "local stationarity",
      "exponential",
      "passage times",
      "macroscopic scale"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}