{
  "id": "1907.10160",
  "version": "v1",
  "published": "2019-07-23T22:24:21.000Z",
  "updated": "2019-07-23T22:24:21.000Z",
  "title": "Uniform convergence to the Airy line ensemble",
  "authors": [
    "Duncan Dauvergne",
    "Mihai Nica",
    "Bálint Virág"
  ],
  "comment": "48 pages, 6 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to show convergence of nonintersecting Bernoulli random walks in all feasible directions in the parameter space. We then use coupling arguments to extend convergence to other models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-23T22:24:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "airy line ensemble",
      "uniform convergence",
      "nonintersecting bernoulli random walks",
      "related nonintersecting random walks converge",
      "core approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}