{
  "id": "2106.07589",
  "version": "v1",
  "published": "2021-06-14T16:49:04.000Z",
  "updated": "2021-06-14T16:49:04.000Z",
  "title": "Gaussian Unitary Ensemble in random lozenge tilings",
  "authors": [
    "Amol Aggarwal",
    "Vadim Gorin"
  ],
  "comment": "24 pages, 7 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "This paper establishes a universality result for scaling limits of uniformly random lozenge tilings of large domains. We prove that whenever a boundary of the domain has three adjacent straight segments inclined under 120 degrees to each other, the asymptotics of tilings near the middle segment is described by the GUE--corners process of random matrix theory. An important step in our argument is to show that fluctuations of the height function of random tilings on essentially arbitrary simply-connected domains of diameter $N$ have smaller magnitude than $N^{1/2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-14T16:49:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian unitary ensemble",
      "uniformly random lozenge tilings",
      "random matrix theory",
      "adjacent straight segments",
      "essentially arbitrary simply-connected domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}