{
  "id": "math-ph/0301039",
  "version": "v4",
  "published": "2003-01-28T21:03:11.000Z",
  "updated": "2003-11-11T15:19:51.000Z",
  "title": "Stochastic Loewner Evolution and Dyson's Circular Ensembles",
  "authors": [
    "John Cardy"
  ],
  "comment": "8 pages. v.2: main result confirmed using conformal field theory; subtle square root elucidated; figures added. v.3: funding acknowledgements added. v.4: erratum to published paper added: this exposes more fully the relation to CFT results",
  "journal": "J. Phys. A 36, L379, 2003; erratum J.Phys. A, 36, 12343, 2003",
  "doi": "10.1088/0305-4470/36/49/c01",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "Stochastic Loewner Evolution (SLE_kappa) has been introduced as a description of the continuum limit of cluster boundaries in two-dimensional critical systems. We show that the problem of N radial SLEs in the unit disc is equivalent to Dyson's Brownian motion on the boundary of the disc, with parameter beta=4/kappa. As a result various equilibrium critical models give realisations of circular ensembles with beta different from the classical values of 1,2 and 4 which correspond to symmetry classes of random U(N) matrices. Some of the bulk critical exponents are related to the spectrum of the associated Calogero-Sutherland hamiltonian. The main result is also checked against the predictions of conformal field theory.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-11-11T15:19:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic loewner evolution",
      "dysons circular ensembles",
      "conformal field theory",
      "dysons brownian motion",
      "continuum limit"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2003,
      "month": "Dec",
      "volume": 36,
      "number": 49,
      "pages": 12343
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003JPhA...3612343C"
    }
  }
}