{
  "id": "1812.00311",
  "version": "v1",
  "published": "2018-12-02T02:50:09.000Z",
  "updated": "2018-12-02T02:50:09.000Z",
  "title": "Basic properties of the Airy line ensemble",
  "authors": [
    "Duncan Dauvergne",
    "Bálint Virág"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper to make it more accessible to probabilists. The two main theorems are a representation in terms of independent Brownian bridges connecting a fine grid of points, and a modulus of continuity result for all lines. Along the way, we give tail bounds and moduli of continuity for nonintersecting ensembles, and a quick proof for the tightness for Dyson's Brownian motion converging to the Airy line ensemble.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-02T02:50:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "airy line ensemble",
      "basic properties",
      "random matrix theory",
      "dysons brownian motion",
      "determinantal formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}