{
  "id": "0802.3654",
  "version": "v1",
  "published": "2008-02-25T17:12:30.000Z",
  "updated": "2008-02-25T17:12:30.000Z",
  "title": "Random walk on a discrete torus and random interlacements",
  "authors": [
    "David Windisch"
  ],
  "comment": "12 pages, accepted for publication in Electronic Communications in Probability",
  "journal": "Electronic Communications in Probability 2008, Vol. 13, 140-150",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)^d, d >= 3, until u N^d time steps, u > 0, and the model of random interlacements recently introduced by Sznitman. In particular, we show that for large N, the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to time u N^d converges to independent copies of the random interlacement at level u.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-25T17:12:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60K35",
      "82C41"
    ],
    "keywords": [
      "random interlacement",
      "discrete torus",
      "local picture left",
      "simple random walk",
      "distant points left"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.3654W"
    }
  }
}