{
  "id": "1105.5105",
  "version": "v2",
  "published": "2011-05-25T18:22:41.000Z",
  "updated": "2012-05-08T21:43:34.000Z",
  "title": "Random walks in degenerate random environments",
  "authors": [
    "Mark Holmes",
    "Thomas S. Salisbury"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic behaviour of random walks in i.i.d. random environments on $\\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2-valued environment, and show that this does not hold for 3-valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong, but non-trivial conditions on the distribution of the environment. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience, and in 2-dimensions the existence of a deterministic limiting velocity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-08T21:43:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37"
    ],
    "keywords": [
      "degenerate random environments",
      "random walks",
      "directional transience",
      "deterministic limiting velocity",
      "asymptotic behaviour"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5105H"
    }
  }
}