{
  "id": "1209.3178",
  "version": "v2",
  "published": "2012-09-14T13:17:41.000Z",
  "updated": "2014-01-27T11:31:21.000Z",
  "title": "Particle Systems with Repulsion Exponent $β$ and Random Matrices",
  "authors": [
    "Martin Venker"
  ],
  "comment": "12 pages; has been rewritten as a note",
  "journal": "Electron. Commun. Probab. 18, no. 83, 1-12, 2013",
  "doi": "10.1214/ECP.v18-2864",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a class of particle systems generalizing the $\\beta$-Ensembles from random matrix theory. In these new ensembles, particles experience repulsion of power $\\beta>0$ when getting close, which is the same as in the $\\beta$-Ensembles. For distances larger than zero, the interaction is allowed to differ from those present for random eigenvalues. We show that the local bulk correlations of the $\\beta$-Ensembles, universal in random matrix theory, also appear in these new ensembles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-27T11:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "82C22"
    ],
    "keywords": [
      "particle systems",
      "random matrices",
      "repulsion exponent",
      "random matrix theory",
      "local bulk correlations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3178V"
    }
  }
}