{
  "id": "1908.11273",
  "version": "v1",
  "published": "2019-08-29T14:58:53.000Z",
  "updated": "2019-08-29T14:58:53.000Z",
  "title": "The stochastic Airy operator at large temperature",
  "authors": [
    "Laure Dumaz",
    "Cyril Labbé"
  ],
  "comment": "40 pages, 4 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It was shown in [J. A. Ram\\'irez, B. Rider and B. Vir\\'ag. J. Amer. Math. Soc. 24, 919-944 (2011)] that the edge of the spectrum of $\\beta$ ensembles converges in the large $N$ limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature $1/\\beta$ goes to $\\infty$: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on $\\mathbb{R}$ of intensity $e^x dx$ and that the eigenfunctions converge to Dirac masses centered at IID points with exponential laws. Furthermore, we obtain a precise description of the microscopic behavior of the eigenfunctions near their localization centers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-29T14:58:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic airy operator",
      "large temperature",
      "poisson point process",
      "dirac masses",
      "appropriately rescaled eigenvalues converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}