{
  "id": "2502.00942",
  "version": "v1",
  "published": "2025-02-02T22:26:41.000Z",
  "updated": "2025-02-02T22:26:41.000Z",
  "title": "Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights",
  "authors": [
    "Tom Alberts",
    "Riddhipratim Basu",
    "Sean Groathouse",
    "Xiao Shen"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation limit for the midpoint transversal fluctuations in a general last-passage percolation (LPP) model with mild assumption on the i.i.d. weights. The rate function is expressed in terms of the right tail large deviation rate function of the last-passage value and the shape function. When the weights are chosen to be i.i.d. exponential random variables, our result verifies a conjecture communicated to us by Liu [Liu'22], showing the asymptotic probability of the geodesic from $(0,0)$ to $(n,n)$ following the corner path $(0,0) \\to (n,0) \\to (n,n)$ is $({4}/{e^2})^{n+o(n)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-02T22:26:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37"
    ],
    "keywords": [
      "geodesic midpoint fluctuations",
      "last-passage percolation",
      "tail large deviation rate function",
      "right tail large deviation rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}