{
  "id": "1804.08587",
  "version": "v1",
  "published": "2018-04-23T17:30:48.000Z",
  "updated": "2018-04-23T17:30:48.000Z",
  "title": "The random normal matrix model: insertion of a point charge",
  "authors": [
    "Yacin Ameur",
    "Nam-Gyu Kang",
    "Seong-Mi Seo"
  ],
  "categories": [
    "math-ph",
    "math.CV",
    "math.MP",
    "math.PR"
  ],
  "abstract": "In this article, we study microscopic properties of a two-dimensional eigenvalue ensemble near a conical singularity arising from insertion of a point charge in the bulk of the support of eigenvalues. In particular, we characterize all rotationally symmetric scaling limits ('Mittag-Leffler fields') and obtain universality of them when the underlying potential is algebraic. Applications include a result on the asymptotic distribution of $\\log|p_n(\\zeta)|$ where $p_n$ is the characteristic polynomial of an $n$:th order random normal matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T17:30:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random normal matrix model",
      "point charge",
      "th order random normal matrix",
      "study microscopic properties",
      "asymptotic distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}