{
  "id": "math/0607162",
  "version": "v2",
  "published": "2006-07-06T13:10:34.000Z",
  "updated": "2011-02-23T11:52:57.000Z",
  "title": "The bead model and limit behaviors of dimer models",
  "authors": [
    "Cédric Boutillier"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AOP398 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 1, 107-142",
  "doi": "10.1214/08-AOP398",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we study the bead model: beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two consecutive beads on a wire; there must be exactly one bead on each neighboring wire. We construct a one-parameter family of Gibbs measures on the bead configurations that are uniform in a certain sense. When endowed with one of these measures, this model is shown to be a determinantal point process, whose marginal on each wire is the sine process (given by eigenvalues of large hermitian random matrices). We prove then that this process appears as a limit of any dimer model on a planar bipartite graph when some weights degenerate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-23T11:52:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimer model",
      "bead model",
      "limit behaviors",
      "large hermitian random matrices",
      "parallel straight lines"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7162B"
    }
  }
}