{
  "id": "1712.04889",
  "version": "v1",
  "published": "2017-12-13T17:58:40.000Z",
  "updated": "2017-12-13T17:58:40.000Z",
  "title": "The Edge Universality of Correlated Matrices",
  "authors": [
    "Arka Adhikari",
    "Ziliang Che"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Gaussian random matrix with correlated entries that have a power law decay of order $d>2$ and prove universality for the extreme eigenvalues. A local law is proved using the self-consistent equation combined with a decomposition of the matrix. This local law along with concentration of eigenvalues around the edge allows us to get an bound for extreme eigenvalues. Using a recent result of the Dyson-Brownian motion, we prove universality of extreme eigenvalues.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T17:58:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edge universality",
      "correlated matrices",
      "extreme eigenvalues",
      "local law",
      "power law decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}