{
  "id": "1101.2982",
  "version": "v2",
  "published": "2011-01-15T12:50:59.000Z",
  "updated": "2011-02-21T13:35:13.000Z",
  "title": "Multiple Meixner-Pollaczek polynomials and the six-vertex model",
  "authors": [
    "Martin Bender",
    "Steven Delvaux",
    "Arno B. J. Kuijlaars"
  ],
  "comment": "32 pages, 4 figures. References added",
  "categories": [
    "math.CA",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem. We also provide a Rodrigues formula and closed expressions for the recurrence coefficients. The proof of the main result follows from a connection with the eigenvalues of block Toeplitz matrices, for which we provide some general results of independent interest. The motivation for this paper is the study of a model in statistical mechanics, the so-called six-vertex model with domain wall boundary conditions, in a particular regime known as the free fermion line. We show how the multiple Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-21T13:35:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "six-vertex model",
      "main result",
      "multiple meixner-pollaczek polynomials arise",
      "domain wall boundary conditions",
      "study multiple orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.2982B"
    }
  }
}