{
  "id": "1407.3367",
  "version": "v1",
  "published": "2014-07-12T10:27:28.000Z",
  "updated": "2014-07-12T10:27:28.000Z",
  "title": "A generalized Asymmetric Exclusion Process with $U_q(\\mathfrak{sl}_2)$ stochastic duality",
  "authors": [
    "Gioia Carinci",
    "Cristian Giardina'",
    "Frank Redig",
    "Tomohiro Sasamoto"
  ],
  "comment": "41 pages, 1 figure",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We study a new process, which we call ASEP$(q,j)$, where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $q\\in (0,1)$ and where at most $2j\\in\\mathbb{N}$ particles per site are allowed. The process is constructed from a $(2j+1)$-dimensional representation of a quantum Hamiltonian with $U_q(\\mathfrak{sl}_2)$ invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP$(q,j)$, we prove self-duality with several self-duality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the first $q$-exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from an homogeneous product measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-12T10:27:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized asymmetric exclusion process",
      "stochastic duality",
      "quantum hamiltonian",
      "one-dimensional integer lattice",
      "step initial conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3367C"
    }
  }
}