{
  "id": "2405.14924",
  "version": "v1",
  "published": "2024-05-23T17:57:06.000Z",
  "updated": "2024-05-23T17:57:06.000Z",
  "title": "Upper tail large deviations of the directed landscape",
  "authors": [
    "Sayan Das",
    "Duncan Dauvergne",
    "Bálint Virág"
  ],
  "comment": "62 pages, 2 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Starting from one-point tail bounds, we establish an upper tail large deviation principle for the directed landscape at the metric level. Metrics of finite rate are in one-to-one correspondence with measures supported on a set of countably many paths, and the rate function is given by a certain Kruzhkov entropy of these measures. As an application of our main result, we prove a large deviation principle for the directed geodesic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-23T17:57:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed landscape",
      "upper tail large deviation principle",
      "one-point tail bounds",
      "main result",
      "kruzhkov entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}