{
  "id": "1810.02538",
  "version": "v1",
  "published": "2018-10-05T06:51:11.000Z",
  "updated": "2018-10-05T06:51:11.000Z",
  "title": "Large deviations for the largest eigenvalue of the sum of two random matrices",
  "authors": [
    "Alice Guionnet",
    "Mylène Maïda"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider the addition of two matrices in generic position, namely A + U BU * , where U is drawn under the Haar measure on the unitary or the orthogonal group. We show that, under mild conditions on the empirical spectral measures of the deterministic matrices A and B, the law of the largest eigenvalue satisfies a large deviation principle, in the scale N, with an explicit rate function involving the limit of spherical integrals. We cover in particular all the cases when A and B have no outliers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-05T06:51:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrices",
      "explicit rate function",
      "large deviation principle",
      "largest eigenvalue satisfies",
      "empirical spectral measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}