{
  "id": "1811.06475",
  "version": "v1",
  "published": "2018-11-15T17:08:11.000Z",
  "updated": "2018-11-15T17:08:11.000Z",
  "title": "The q-Hahn PushTASEP",
  "authors": [
    "Ivan Corwin",
    "Konstantin Matveev",
    "Leonid Petrov"
  ],
  "comment": "27 pages, 3 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We introduce the q-Hahn PushTASEP --- an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The transition probabilities in the q-Hahn PushTASEP are expressed through the ${}_4\\phi_3$ basic hypergeometric function. Under suitable limits, the q-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the q-Hahn TASEP introduced by Povolotsky (arXiv:1308.3250). We establish Markov duality relations and contour integral formulas for the q-Hahn PushTASEP. We also take a $q\\to1$ limit of our process arriving at a new beta polymer-like model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-15T17:08:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "totally asymmetric simple exclusion process",
      "basic hypergeometric function",
      "integrable stochastic interacting particle system",
      "q-hahn pushtasep degenerates",
      "establish markov duality relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}