{
  "id": "2407.20835",
  "version": "v1",
  "published": "2024-07-30T14:04:26.000Z",
  "updated": "2024-07-30T14:04:26.000Z",
  "title": "Limit fluctuations of stationary measures of totally asymmetric simple exclusion processes with open boundaries on the coexistence line",
  "authors": [
    "Włodzimierz Bryc",
    "Joseph Najnudel",
    "Yizao Wang"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We characterize limit fluctuations of height functions of the totally asymmetric simple exclusion processes with open boundaries at the co-existence line under the stationary measures. The limit behavior of the height functions at the co-existence line was known to be exotic in the sense that the first-order limit theorem (when divided by $n$) has a random limit. Here, we show that with a random centering and then divided by $\\sqrt n$, the second-order limit of the height functions is a (random) mixture of two independent Brownian motions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-30T14:04:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "totally asymmetric simple exclusion processes",
      "stationary measures",
      "limit fluctuations",
      "open boundaries",
      "coexistence line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}