{
  "id": "2304.14380",
  "version": "v1",
  "published": "2023-04-27T17:49:10.000Z",
  "updated": "2023-04-27T17:49:10.000Z",
  "title": "Spacetime limit shapes of the KPZ equation in the upper tails",
  "authors": [
    "Yier Lin",
    "Li-Cheng Tsai"
  ],
  "comment": "22 pages, 4 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the $n$-point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a wide range of scaling regimes that allows time to be short, unit-order, and long. We prove the $n$-point large deviation principle and characterize, with proof, the corresponding spacetime limit shape. Our proof is based on the results -- from the companion paper Tsai (2023) -- on moments of the stochastic heat equation and utilizes ideas coming from a tree decomposition. Behind our proof lies the phenomenon where the major contribution of the noise concentrates around certain corridors in spacetime, and we explicitly describe the corridors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-27T17:49:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kpz equation",
      "upper tails",
      "point large deviation principle",
      "narrow wedge initial condition",
      "corresponding spacetime limit shape"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}