{
  "id": "1612.00917",
  "version": "v1",
  "published": "2016-12-03T03:14:09.000Z",
  "updated": "2016-12-03T03:14:09.000Z",
  "title": "Average Entropy of the Ranges for Simple Random Walks on Discrete Groups",
  "authors": [
    "Xin-Xing Chen",
    "Jian-Sheng Xie",
    "Min-Zhi Zhao"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Inspired by Benjamini et al (Ann. Inst. H. Poincar\\'e Probab. Stat. 2010) and Windisch (Electron. J. Probab. 2010), we consider the entropy of the random walk range formed by a simple random walk on a discrete group. It is shown in this setting the existence of a quantity which we call the average entropy of the range. The extreme values of this quantity are also discussed. An important consequence is that, the tail $\\sigma$-algebra formed by the $n$-step ranges is always trivial for a recurrent random walk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-03T03:14:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J05"
    ],
    "keywords": [
      "simple random walk",
      "discrete group",
      "average entropy",
      "recurrent random walk",
      "random walk range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}