{
  "id": "2212.07349",
  "version": "v1",
  "published": "2022-12-14T17:22:41.000Z",
  "updated": "2022-12-14T17:22:41.000Z",
  "title": "Markov duality and Bethe ansatz formula for half-line open ASEP",
  "authors": [
    "Guillaume Barraquand",
    "Ivan Corwin"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Using a Markov duality satisfied by ASEP on the integer line, we deduce a similar Markov duality for half-line open ASEP and open ASEP on a segment. This leads to closed systems of ODEs characterizing observables of the models. In the half-line case, we solve the system of ODEs using Bethe ansatz and prove an integral formula for $q$-moments of the current at $n$ distinct spatial locations. We then use this formula to confirm predictions for the moments of the multiplicative noise stochastic heat equation on $\\mathbb R_{>0}$ with Robin type boundary condition and we obtain new formulas in the case of a Dirichlet boundary condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-14T17:22:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "half-line open asep",
      "markov duality",
      "bethe ansatz formula",
      "robin type boundary condition",
      "multiplicative noise stochastic heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}