{
  "id": "1901.04673",
  "version": "v1",
  "published": "2019-01-15T06:23:53.000Z",
  "updated": "2019-01-15T06:23:53.000Z",
  "title": "Biased random walk on the trace of biased random walk on the trace of...",
  "authors": [
    "David Croydon",
    "Mark Holmes"
  ],
  "comment": "36 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is the trace of the (i - 1)-st walk. The sequence of bias vectors is chosen so that each walk is transient. We prove the aforementioned transience and a law of large numbers, and provide criteria for ballisticity and sub-ballisticity. We give examples of sequences of biases for which each X(i), i>=1 is (transient but) not ballistic, and the limiting graph is an infinite simple (self-avoiding) path. We also give examples for which each X(i), i>=1 is ballistic, but the limiting graph is not a simple path.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T06:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60G50",
      "60K35",
      "82B26",
      "82B41"
    ],
    "keywords": [
      "biased random walk",
      "limiting graph",
      "random graphs",
      "infinite simple",
      "initial graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}