{
  "id": "1708.03270",
  "version": "v1",
  "published": "2017-08-10T15:45:29.000Z",
  "updated": "2017-08-10T15:45:29.000Z",
  "title": "Self-trapping self-repelling random walks",
  "authors": [
    "Peter Grassberger"
  ],
  "comment": "5 pages main paper + 5 pages supplementary material",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Although the title seems self-contradictory, it does not contain a misprint. The model we study is a seemingly minor modification of the \"true self-avoiding walk\" (TSAW) model of Amit, Parisi, and Peliti in two dimensions. The walks in it are self-repelling up to a characteristic time $T^*$ (which depends on various parameters), but spontaneously (i.e., without changing any control parameter) become self-trapping after that. For free walks, $T^*$ is astronomically large, but on finite lattices the transition is easily observable. In the self-trapped regime, walks are subdiffusive and intermittent, spending longer and longer times in small areas until they escape and move rapidly to a new area. In spite of this, these walks are extremely efficient in covering finite lattices, as measured by average cover times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-10T15:45:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-trapping self-repelling random walks",
      "finite lattices",
      "average cover times",
      "small areas",
      "seemingly minor modification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}