{
  "id": "1403.1571",
  "version": "v1",
  "published": "2014-03-06T20:52:11.000Z",
  "updated": "2014-03-06T20:52:11.000Z",
  "title": "Martingale defocusing and transience of a self-interacting random walk",
  "authors": [
    "Yuval Peres",
    "Bruno Schapira",
    "Perla Sousi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Suppose that $(X,Y,Z)$ is a random walk in $\\mathbb{Z}^3$ that moves in the following way: on the first visit to a vertex only $Z$ changes by $\\pm 1$ equally likely, while on later visits to the same vertex $(X,Y)$ performs a two-dimensional random walk step. We show that this walk is transient thus answering a question of Benjamini, Kozma and Schapira. One important ingredient of the proof is a dispersion result for martingales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-06T20:52:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "self-interacting random walk",
      "martingale defocusing",
      "transience",
      "two-dimensional random walk step",
      "dispersion result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.1571P"
    }
  }
}