{
  "id": "1901.09257",
  "version": "v1",
  "published": "2019-01-26T18:18:48.000Z",
  "updated": "2019-01-26T18:18:48.000Z",
  "title": "Uniqueness of the Gaussian Orthogonal Ensemble",
  "authors": [
    "Jose Angel Sanchez Gomez",
    "Victor Amaya Carvajal"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "It is not hard to prove that, given a random Wigner matrix $X$ that belongs to the Gaussian Orthogonal Ensemble (GOE), then $X$ is invariant under orthogonal conjugations. Our aim is to prove that if $X$ is a random symmetric matrix that is invariant under orthogonal transformations then such matrix $X$ belongs to the GOE. We will to this using nothing more than the characteristic function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-26T18:18:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian orthogonal ensemble",
      "uniqueness",
      "random wigner matrix",
      "random symmetric matrix",
      "orthogonal transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}