{
  "id": "2205.13029",
  "version": "v1",
  "published": "2022-05-25T19:47:55.000Z",
  "updated": "2022-05-25T19:47:55.000Z",
  "title": "Shift invariance of half space integrable models",
  "authors": [
    "Jimmy He"
  ],
  "comment": "64 pages, 15 figures. Comments welcome!",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six vertex model in a half space, from which we obtain results on the asymmetric simple exclusion process, as well as for the beta polymer through a fusion procedure which may be of independent interest. As an application, we establish a distributional identity between the absorption time in a type $B$ analogue of the oriented swap process and last passage times in a half space, establishing the Baik--Ben Arous--P\\'ech\\'e phase transition for the absorption time. The proof uses Hecke algebras and integrability of the six vertex model through the Yang--Baxter and reflection equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-25T19:47:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C23",
      "60K35",
      "82C22"
    ],
    "keywords": [
      "half space integrable models",
      "shift invariance",
      "absorption time",
      "asymmetric simple exclusion process",
      "baik-ben arous-peche phase transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}