{
  "id": "2004.14068",
  "version": "v1",
  "published": "2020-04-29T10:42:08.000Z",
  "updated": "2020-04-29T10:42:08.000Z",
  "title": "Local Geometry of the rough-smooth interface in the two-periodic Aztec diamond",
  "authors": [
    "Vincent Beffara",
    "Sunil Chhita",
    "Kurt Johansson"
  ],
  "comment": "50 pages, 7 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture at this interface by introducing well-defined lattice paths which are closely related to the level lines of the height function. We show, after suitable centering and rescaling, that a point process from these paths converge to the extended Airy kernel point process provided that the natural parameter associated to the two-periodic Aztec diamond is small enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-29T10:42:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-periodic aztec diamond",
      "rough-smooth interface",
      "extended airy kernel point process",
      "local geometry",
      "dominoes decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}