{
  "id": "1807.11117",
  "version": "v1",
  "published": "2018-07-29T22:48:20.000Z",
  "updated": "2018-07-29T22:48:20.000Z",
  "title": "Percolation for level-sets of Gaussian free fields on metric graphs",
  "authors": [
    "Jian Ding",
    "Mateo Wirth"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity and the bound is sharp up to a poly-logarithmic factor with an exponent of one-quarter. This substantially improves a previous result by Li and the first author. In three dimensions and higher, we provide rather sharp estimates of percolation probabilities in different regimes which altogether describe a sharp phase transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-29T22:48:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G60",
      "60K35"
    ],
    "keywords": [
      "gaussian free fields",
      "metric graphs",
      "study level-set percolation",
      "sharp phase transition",
      "macroscopic annulus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}