{
  "id": "1705.01980",
  "version": "v1",
  "published": "2017-05-04T19:18:15.000Z",
  "updated": "2017-05-04T19:18:15.000Z",
  "title": "Dynamic ASEP, duality and continuous $q^{-1}$-Hermite polynomials",
  "authors": [
    "Alexei Borodin",
    "Ivan Corwin"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We demonstrate a Markov duality between the dynamic ASEP and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While investigating the duality for half-stationary initial data, we uncover and utilize connections to continuous $q^{-1}$-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with these $q^{-1}$-Hermite polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-04T19:18:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hermite polynomials",
      "dynamic asep",
      "half-stationary initial data",
      "step initial data",
      "continuous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}