{
  "id": "2108.11424",
  "version": "v1",
  "published": "2021-08-25T18:36:54.000Z",
  "updated": "2021-08-25T18:36:54.000Z",
  "title": "A zero-one law for random walks in random environments on $\\mathbb{Z}^2$ with bounded jumps",
  "authors": [
    "Daniel J. Slonim"
  ],
  "comment": "24 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Zerner and Merkl proved a 0-1 law for directional transience for planar random walks in random environments. Later, Zerner provided a simplified proof. We extend the result to non-planar i.i.d. random walks in random environments on $\\Z^2$ with bounded jumps. As an application, we complete a characterization of directional transience (for a given direction) for random walks in Dirichlet environments with bounded jumps in all dimensions. Such a characterization was previously known for the nearest-neighbor case of Dirichlet environments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-25T18:36:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J10",
      "60K37"
    ],
    "keywords": [
      "random environments",
      "bounded jumps",
      "zero-one law",
      "directional transience",
      "dirichlet environments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}