{
  "id": "2112.12096",
  "version": "v2",
  "published": "2021-12-22T17:58:19.000Z",
  "updated": "2023-11-27T13:13:07.000Z",
  "title": "First passage percolation with long-range correlations and applications to random Schrödinger operators",
  "authors": [
    "Sebastian Andres",
    "Alexis Prévost"
  ],
  "comment": "54 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\\mathbb{Z}^d$, $d\\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\\nabla \\phi$ interface models or random interlacements as prominent examples. We show that the associated time constant is positive, the FPP distance is comparable to the Euclidean distance, and we obtain a shape theorem. We also present two applications for random conductance models (RCM) with possibly unbounded and strongly correlated conductances. Namely, we obtain a Gaussian heat kernel upper bound for RCMs with a general class of speed measures, and an exponential decay estimate for the Green function of RCMs with random killing measures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-11-27T13:13:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "39A12",
      "82B43",
      "60J35",
      "82C41"
    ],
    "keywords": [
      "first passage percolation",
      "random schrödinger operators",
      "long-range correlations",
      "gaussian heat kernel upper bound",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}