{
  "id": "2410.19070",
  "version": "v1",
  "published": "2024-10-24T18:26:52.000Z",
  "updated": "2024-10-24T18:26:52.000Z",
  "title": "The directed landscape seen from its trees",
  "authors": [
    "Mustazee Rahman",
    "Balint Virag"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reconstructed from the shapes of its semi-infinite geodesics. In order to show this result, we make use of the Busemann process of the directed landscape together with a novel ``coordinate system\" and ``differential distance\" to capture the behaviour of semi-infinite geodesics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-24T18:26:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed landscape",
      "semi-infinite geodesics",
      "basic question",
      "differential distance",
      "busemann process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}