{
  "id": "1401.3321",
  "version": "v1",
  "published": "2014-01-14T20:27:05.000Z",
  "updated": "2014-01-14T20:27:05.000Z",
  "title": "The $(q,μ,ν)$-Boson process and $(q,μ,ν)$-TASEP",
  "authors": [
    "Ivan Corwin"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We prove a intertwining relation (or Markov duality) between the $(q,\\mu,\\nu)$-Boson process and $(q,\\mu,\\nu)$-TASEP, two discrete time Markov chains introduced by Povolotsky. Using this and a variant of the coordinate Bethe ansatz we compute nested contour integral formulas for expectations of a family of observables of the $(q,\\mu,\\nu)$-TASEP when started from step initial data. We then utilize these to prove a Fredholm determinant formula for distribution of the location of any given particle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-14T20:27:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boson process",
      "discrete time markov chains",
      "coordinate bethe ansatz",
      "nested contour integral formulas",
      "step initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.3321C"
    }
  }
}