{
  "id": "math-ph/0610050",
  "version": "v1",
  "published": "2006-10-20T18:16:54.000Z",
  "updated": "2006-10-20T18:16:54.000Z",
  "title": "Asymptotic analysis of random matrices with external source and a family of algebraic curves",
  "authors": [
    "K. D. T-R McLaughlin"
  ],
  "doi": "10.1088/0951-7715/20/7/002",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a particular algebraic curve. For the case of a quartic external field, the curve in question is proven to exist, yielding precise asymptotic information about the limiting mean density of eigenvalues, as well as bulk and edge universality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-20T18:16:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic curve",
      "random matrices",
      "external source",
      "complete asymptotic analysis",
      "yielding precise asymptotic information"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}