{
  "id": "1504.03605",
  "version": "v1",
  "published": "2015-04-14T16:19:16.000Z",
  "updated": "2015-04-14T16:19:16.000Z",
  "title": "Convergence of local statistics of Dyson Brownian motion",
  "authors": [
    "Benjamin Landon",
    "Horng-Tzer Yau"
  ],
  "comment": "38 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We analyze the rate of convergence of the local statistics of Dyson Brownian motion to the GOE/GUE for short times $t=o(1)$ with deterministic initial data V . Our main result states that if the density of states of $V$ is bounded both above and away from $0$ down to scales $\\ell \\ll t$ in a small interval of size $G \\gg \\sqrt{t}$ around an energy $E_0$, then the local statistics coincide with the GOE/GUE near the energy $E_0$ after time $t$. Our methods are partly based on the idea of coupling two Dyson Brownian motions from [6], the parabolic regularity result of [15], and the eigenvalue rigidity results of [21].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-14T16:19:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dyson brownian motion",
      "convergence",
      "parabolic regularity result",
      "deterministic initial data",
      "main result states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403605L"
    }
  }
}