{
  "id": "1204.5297",
  "version": "v2",
  "published": "2012-04-24T08:27:33.000Z",
  "updated": "2014-01-30T16:37:00.000Z",
  "title": "Type transition of simple random walks on randomly directed regular lattices",
  "authors": [
    "Massimo Campanino",
    "Dimitri Petritis"
  ],
  "comment": "Accepted for publication in Journal of Applied Probability (2014)",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Simple random walks on a partially directed version of $\\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function, the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of the simple random walk, i.e.\\ its being recurrent or transient, and show that there exists a critical value of the decay power, above which the walk is almost surely recurrent and below which is almost surely transient.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-30T16:37:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K20"
    ],
    "keywords": [
      "simple random walk",
      "randomly directed regular lattices",
      "type transition",
      "perturbation probability decays",
      "decay power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5297C"
    }
  }
}