{
  "id": "1512.02790",
  "version": "v1",
  "published": "2015-12-09T08:53:29.000Z",
  "updated": "2015-12-09T08:53:29.000Z",
  "title": "Mixing time for the random walk on the range of the random walk on tori",
  "authors": [
    "Jiří Černý",
    "Artem Sapozhnikov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the subgraph of the discrete $d$-dimensional torus of size length $N$, $d\\ge3$, induced by the range of the simple random walk on the torus run until the time $uN^d$. We prove that for all $d\\ge 3$ and $u>0$, the mixing time for the random walk on this subgraph is of order $N^2$ with probability at least $1 - Ce^{-(\\log N)^2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-09T08:53:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "58J35"
    ],
    "keywords": [
      "mixing time",
      "simple random walk",
      "dimensional torus",
      "torus run",
      "size length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}