{
  "id": "1603.06761",
  "version": "v1",
  "published": "2016-03-22T12:35:21.000Z",
  "updated": "2016-03-22T12:35:21.000Z",
  "title": "On bulk singularities in the random normal matrix model",
  "authors": [
    "Yacin Ameur",
    "Seong-Mi Seo"
  ],
  "categories": [
    "math-ph",
    "math.CV",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e. a point in the interior of the droplet where the density of the classical equilibrium measure vanishes. We prove results to the effect that a certain \"dominant part\" of the Taylor expansion determines the microscopic properties near a bulk singularity. A description of the distribution is given in terms of a special entire function, which depends on the nature of the singularity (a Mittag-Leffler function in the case of a rotationally symmetric singularity).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-22T12:35:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random normal matrix model",
      "bulk singularity",
      "classical equilibrium measure vanishes",
      "special entire function",
      "taylor expansion determines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}