{
  "id": "0708.3867",
  "version": "v1",
  "published": "2007-08-28T22:51:48.000Z",
  "updated": "2007-08-28T22:51:48.000Z",
  "title": "Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane",
  "authors": [
    "Alexander R. Its",
    "Leon A. Takhtajan"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We introduce a dbar-formulation of the orthogonal polynomials on the complex plane, and hence of the related normal matrix model, which is expected to play the same role as the Riemann-Hilbert formalism in the theory of orthogonal polynomials on the line and for the related Hermitian model. We propose an analog of Deift-Kriecherbauer-McLaughlin-Venakides-Zhou asymptotic method for the analysis of the relevant dbar-problem, and indicate how familiar steps for the Hermitian model, e.g. the g-function ``undressing'', might look like in the case of the normal model. We use the particular model considered recently by P. Elbau and G. Felder as a case study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-28T22:51:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orthogonal polynomials",
      "complex plane",
      "deift-kriecherbauer-mclaughlin-venakides-zhou asymptotic method",
      "related normal matrix model",
      "related hermitian model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3867I"
    }
  }
}