{
  "id": "1810.00564",
  "version": "v1",
  "published": "2018-10-01T07:40:39.000Z",
  "updated": "2018-10-01T07:40:39.000Z",
  "title": "Weak limits of the measures of maximal entropy for Orthogonal polynomials",
  "authors": [
    "Carsten Lunde Petersen",
    "Eva Uhre"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study the sequence of orthonormal polynomials $\\{P_n(\\mu; z)\\}$ defined by a probability measure $\\mu$ with non-polar compact support $S(\\mu)\\subset\\mathbb C$. We show that the support of any weak* limit of the sequence of measures of maximal entropy $\\omega_n$ for $P_n$ is contained in the polynomial-convex hull of $S(\\mu)$. And for $n$-th root regular measures the $\\omega_n$ converge weak* to the equilibrium measure on $S(\\mu)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T07:40:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C05",
      "37F10",
      "31A15"
    ],
    "keywords": [
      "maximal entropy",
      "orthogonal polynomials",
      "weak limits",
      "th root regular measures",
      "non-polar compact support"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}