{
  "id": "0705.2671",
  "version": "v1",
  "published": "2007-05-18T10:54:35.000Z",
  "updated": "2007-05-18T10:54:35.000Z",
  "title": "Hidden Symmetries of Stochastic Models",
  "authors": [
    "Boyka Aneva"
  ],
  "comment": "This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 3 (2007), 068, 12 pages",
  "doi": "10.3842/SIGMA.2007.068",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n)$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n)$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-18T10:54:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic models",
      "hidden symmetries",
      "asymmetric simple exclusion process generate",
      "parameter dependent linear terms",
      "matrix product states approach"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2007,
      "month": "May",
      "volume": 3,
      "pages": "068"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007SIGMA...3..068A"
    }
  }
}