{
  "id": "1205.0671",
  "version": "v3",
  "published": "2012-05-03T10:21:27.000Z",
  "updated": "2014-10-27T13:32:48.000Z",
  "title": "Local universality of repulsive particle systems and random matrices",
  "authors": [
    "F. Götze",
    "M. Venker"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/13-AOP844 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2014, Vol. 42, No. 6, 2207-2242",
  "doi": "10.1214/13-AOP844",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or determinantal representation, the local correlations in the bulk coincide in the limit of infinitely many particles with those known from random Hermitian matrices; in particular they can be expressed as determinants of the so-called sine kernel. These results may provide an explanation for the appearance of sine kernel correlation statistics in a number of situations which do not have an obvious interpretation in terms of random matrices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-04T20:59:26.000Z",
      "title": "Local Universality of Repulsive Particle Systems and Random Matrices",
      "abstract": "We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or determinantal representation, the local correlations in the bulk coincide in the limit of infinitely many particles with those known from random Hermitian matrices, in particular they can be expressed as determinants of the so-called sine kernel. These results may provide an explanation for the appearance of sine kernel correlation statistics in a number of situations which do not have an obvious interpretation in terms of random matrices.",
      "comment": "Some typos have been corrected, some changes made in the introduction, the assumption of exponential decay of $\\hat{h}$ has been removed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-27T13:32:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "82C22"
    ],
    "keywords": [
      "repulsive particle systems",
      "random matrices",
      "local universality",
      "random hermitian matrices",
      "sine kernel correlation statistics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0671G"
    }
  }
}