{
  "id": "1804.03414",
  "version": "v2",
  "published": "2018-04-10T09:20:12.000Z",
  "updated": "2018-04-11T13:38:45.000Z",
  "title": "Dimer model, bead model and standard Young tableaux: finite cases and limit shapes",
  "authors": [
    "Wangru Sun"
  ],
  "comment": "67 pages, 15 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "The bead model is a random point field on $\\mathbb{Z}\\times\\mathbb{R}$ which can be viewed as a scaling limit of dimer model. We prove that, in the scaling limit, the normalized height function of a uniformly chosen random bead configuration lies in an arbitrarily small neighborhood of a surface $h_0$ that maximizes some functional which we call as entropy. We also prove that the limit shape $h_0$ is a scaling limit of the limit shapes of a properly chosen sequence of dimer models. There is a map from bead configurations to standard tableaux of a (skew) Young diagram, and the map preserves uniform measures, and our results of the bead model yield the existence of the limit shape of a random standard Young tableau.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-04-11T13:38:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit shape",
      "bead model",
      "standard young tableaux",
      "dimer model",
      "finite cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}