{
  "id": "1404.4265",
  "version": "v1",
  "published": "2014-04-16T14:30:25.000Z",
  "updated": "2014-04-16T14:30:25.000Z",
  "title": "A short proof of a symmetry identity for the $(q,μ,ν)$-deformed Binomial distribution",
  "authors": [
    "Guillaume Barraquand"
  ],
  "comment": "3 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a short and elementary proof of a $(q, \\mu, \\nu)$-deformed Binomial distribution identity arising in the study of the $(q, \\mu, \\nu)$-Boson process and the $(q, \\mu, \\nu)$-TASEP. This identity found by Corwin in [4] was a key technical step to prove an intertwining relation between the Markov transition matrices of these two classes of discrete-time Markov chains. This was used in turn to derive exact formulas for a large class of observables of both these processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-16T14:30:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short proof",
      "symmetry identity",
      "markov transition matrices",
      "discrete-time markov chains",
      "boson process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4265B"
    }
  }
}