{
  "id": "0903.3179",
  "version": "v1",
  "published": "2009-03-18T15:11:04.000Z",
  "updated": "2009-03-18T15:11:04.000Z",
  "title": "Entropy of Random Walk Range",
  "authors": [
    "Itai Benjamini",
    "Gady Kozma",
    "Ariel Yadin",
    "Amir Yehudayoff"
  ],
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study the entropy of the set traced by an $n$-step random walk on $\\Z^d$. We show that for $d \\geq 3$, the entropy is of order $n$. For $d = 2$, the entropy is of order $n/\\log^2 n$. These values are essentially governed by the size of the boundary of the trace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-18T15:11:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05"
    ],
    "keywords": [
      "random walk range",
      "step random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010AnIHP..46.1080B"
    }
  }
}