{
  "id": "1911.03037",
  "version": "v1",
  "published": "2019-11-08T04:14:41.000Z",
  "updated": "2019-11-08T04:14:41.000Z",
  "title": "Phase transitions for degenerate random environments",
  "authors": [
    "Mark Holmes",
    "Thomas S. Salisbury"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a class of models of i.i.d.~random environments in general dimensions $d\\ge 2$, where each site is equipped randomly with an environment, and a parameter $p$ governs the frequency of certain environments that can act as a barrier. We show that many of these models (including some which are non-monotone in $p$) exhibit a sharp phase transition for the geometry of connected clusters as $p$ varies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-08T04:14:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "degenerate random environments",
      "sharp phase transition",
      "general dimensions",
      "non-monotone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}