{
  "id": "2203.02551",
  "version": "v1",
  "published": "2022-03-04T19:57:31.000Z",
  "updated": "2022-03-04T19:57:31.000Z",
  "title": "Proof Methods in Random Matrix Theory",
  "authors": [
    "Michael Fleermann",
    "Werner Kirsch"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this survey article, we give an introduction to two methods of proof in random matrix theory: The method of moments and the Stieltjes transform method. We thoroughly develop these methods and apply them to show both the semicircle law and the Marchenko-Pastur law for random matrices with independent entries. The material is presented in a pedagogical manner and is suitable for anyone who has followed a course in measure-theoretic probability theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-04T19:57:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix theory",
      "proof methods",
      "measure-theoretic probability theory",
      "stieltjes transform method",
      "independent entries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}