{
  "id": "2003.04911",
  "version": "v1",
  "published": "2020-03-10T18:06:51.000Z",
  "updated": "2020-03-10T18:06:51.000Z",
  "title": "The Smallest Eigenvalue Distribution of the Jacobi Unitary Ensembles",
  "authors": [
    "Shulin Lyu",
    "Yang Chen"
  ],
  "comment": "20 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the hard edge scaling limit of the Jacobi unitary ensemble generated by the weight $x^{\\alpha}(1-x)^{\\beta},~x\\in[0,1],~\\alpha,\\beta>0$, the probability that all eigenvalues of Hermitian matrices from this ensemble lie in the interval $[t,1]$ is given by the Fredholm determinant of the Bessel kernel. We derive the constant in the asymptotics of this Bessel-kernel determinant. A specialization of the results gives the constant in the asymptotics of the probability that the interval $(-a,a),a>0,$ is free of eigenvalues in the Jacobi unitary ensemble with the symmetric weight $(1-x^2)^{\\beta}, x\\in[-1,1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-10T18:06:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "34E05",
      "41A60",
      "42C05"
    ],
    "keywords": [
      "jacobi unitary ensemble",
      "smallest eigenvalue distribution",
      "hard edge scaling limit",
      "bessel kernel",
      "bessel-kernel determinant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}