{
  "id": "cond-mat/0402215",
  "version": "v1",
  "published": "2004-02-07T14:30:50.000Z",
  "updated": "2004-02-07T14:30:50.000Z",
  "title": "Random matrix ensembles from nonextensive entropy",
  "authors": [
    "Fabricio Toscano",
    "Raul O. Vallejos",
    "Constantino Tsallis"
  ],
  "comment": "7 pages, including 3 PS figures",
  "doi": "10.1103/PhysRevE.69.066131",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \\int d{\\bf H} [P({\\bf H})] \\ln [P({\\bf H})], with suitable constraints. Here we construct and analyze random-matrix ensembles arising from the generalized entropy S_q = (1 - \\int d{\\bf H} [P({\\bf H})]^q)/(q-1) (thus S_1=S_{BGS}). The resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form. Making q -> 1 recovers the Gaussian ensembles. If q \\ne 1, the joint probability distributions P(\\bf H) cannot be factorized, i.e., the matrix elements of \\bf H are correlated. In the limit of large matrices two different regimes are observed. When q<1, P(\\bf H) has compact support, and the fluctuations tend asymptotically to those of the Gaussian ensembles. Anomalies appear for q>1: Both P(\\bf H) and the marginal distributions P(H_{ij}) show power-law tails. Numerical analyses reveal that the nearest-neighbor spacing distribution is also long-tailed (not Wigner-Dyson) and, after proper scaling, very close to the result for the 2 x 2 case -- a generalization of Wigner's surmise. We discuss connections of these \"nonextensive\" ensembles with other non-Gaussian ones, like the so-called L\\'evy ensembles and those arising from soft-confinement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-07T14:30:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix ensembles",
      "nonextensive entropy",
      "analyze random-matrix ensembles",
      "joint probability distributions",
      "random matrices"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}