{
  "id": "math/0503065",
  "version": "v1",
  "published": "2005-03-03T19:03:28.000Z",
  "updated": "2005-03-03T19:03:28.000Z",
  "title": "Recurrence of Simple Random Walk on $Z^2$ is Dynamically Sensitive",
  "authors": [
    "Christopher Hoffman"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Benjamini, Haggstrom, Peres and Steif introduced the concept of a dynamical random walk. This is a continuous family of random walks, {S_n(t)}. Benjamini et. al. proved that if d=3 or d=4 then there is an exceptional set of t such that {S_n(t)} returns to the origin infinitely often. In this paper we consider a dynamical random walk on Z^2. We show that with probability one there exists t such that {S_n(t)} never returns to the origin. This exceptional set of times has dimension one. This proves a conjecture of Benjamini et. al.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-03T19:03:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple random walk",
      "dynamical random walk",
      "dynamically sensitive",
      "recurrence",
      "exceptional set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3065H"
    }
  }
}