{
  "id": "2103.07816",
  "version": "v1",
  "published": "2021-03-13T23:54:41.000Z",
  "updated": "2021-03-13T23:54:41.000Z",
  "title": "Painlevé V for a Jacobi unitary ensemble with random singularities",
  "authors": [
    "Mengkun Zhu",
    "Chuanzhong Li",
    "Yang Chen"
  ],
  "comment": "Applied Mathematics Letters,2021",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we focus on the relationship between the fifth Painlev\\'{e} equation and a Jacobi weight perturbed with random singularities, \\begin{equation*} w(z)=\\left(1-z^2\\right)^{\\alpha}{\\rm e}^{-\\frac{t}{z^2-k^2}},~~~z,k\\in[-1,1],~\\alpha,t>0. \\end{equation*} By using the ladder operator approach, we obtain that an auxiliary quantity $R_n(t)$, which is closely related to the recurrence coefficients of monic polynomials orthogonal with $w(z)$, satisfies a particular Painlev\\'{e} V equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-13T23:54:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacobi unitary ensemble",
      "random singularities",
      "monic polynomials orthogonal",
      "ladder operator approach",
      "recurrence coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}