{
  "id": "2302.12082",
  "version": "v1",
  "published": "2023-02-23T15:12:43.000Z",
  "updated": "2023-02-23T15:12:43.000Z",
  "title": "Extreme eigenvalues of random matrices from Jacobi ensembles",
  "authors": [
    "B. Winn"
  ],
  "comment": "36 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \\beta $-Ensembles are derived for matrices of large size in the r\\'egime where $ \\beta > 0 $ is arbitrary and one of the model parameters $ \\alpha_1 $ is an integer. By a straightforward transformation this leads to corresponding results for the distribution of the largest eigenvalue. The explicit expressions are given in terms of multi-variable hypergeometric functions, and it is found that the first-order corrections are proportional to the derivative of the leading order limiting distribution function. In some special cases $ \\beta = 2 $ and/or small values of $ \\alpha_1 $, explicit formulae involving more familiar functions, such as the modified Bessel function of the first kind, are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-23T15:12:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "extreme eigenvalues",
      "jacobi ensembles",
      "random matrices",
      "probability distribution functions",
      "leading order limiting distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}