{
  "id": "1203.3459",
  "version": "v1",
  "published": "2012-03-15T19:55:03.000Z",
  "updated": "2012-03-15T19:55:03.000Z",
  "title": "Self-interacting random walks",
  "authors": [
    "Yuval Peres",
    "Serguei Popov",
    "Perla Sousi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\mu_1,... \\mu_k$ be $d$-dimensional probability measures in $\\R^d$ with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-15T19:55:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-interacting random walks",
      "dimensional probability measures",
      "construct examples",
      "recurrent processes",
      "complete picture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.3459P"
    }
  }
}