{
  "id": "2412.09660",
  "version": "v1",
  "published": "2024-12-12T10:08:34.000Z",
  "updated": "2024-12-12T10:08:34.000Z",
  "title": "Comment on the paper \"Exact decay of the persistence probability in the Airy$_1$ process\" by Ferrari and Liu",
  "authors": [
    "Sylvain Prolhac"
  ],
  "comment": "Comment on arXiv:2402.10661 ; 2 pages",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We point out that the non-trivial function obtained by Ferrari and Liu for the persistence probability of the Airy$_1$ process has a strikingly similar form as a large deviation function found earlier by the author for current fluctuations of the totally asymmetric exclusion process with periodic boundaries conditioned on flat initial and final states. A proposed explanation for this observation, which relates similar yet clearly distinct quantities, is that both results pertain to conditioning on the same kind of rare events where a current larger than typical is maintained throughout the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-12T10:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "persistence probability",
      "exact decay",
      "totally asymmetric exclusion process",
      "large deviation function",
      "current larger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}