{
  "id": "1710.03921",
  "version": "v1",
  "published": "2017-10-11T06:17:39.000Z",
  "updated": "2017-10-11T06:17:39.000Z",
  "title": "Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach",
  "authors": [
    "Khanh Duy Trinh"
  ],
  "comment": "to appear in J. Theoret. Probab",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper describes the global limiting behavior of Gaussian beta ensembles where the parameter $\\beta$ is allowed to vary with the matrix size $n$. In particular, we show that as $n \\to \\infty$ with $n\\beta \\to \\infty$, the empirical distribution converges weakly to the semicircle distribution, almost surely. The Gaussian fluctuation around the limit is then derived by a martingale approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-11T06:17:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60F05"
    ],
    "keywords": [
      "gaussian beta ensembles",
      "global spectrum fluctuations",
      "martingale approach",
      "gaussian fluctuation",
      "semicircle distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}