{
  "id": "1502.02831",
  "version": "v1",
  "published": "2015-02-10T09:57:41.000Z",
  "updated": "2015-02-10T09:57:41.000Z",
  "title": "The most visited sites of biased random walks on trees",
  "authors": [
    "Yueyun Hu",
    "Zhan Shi"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the slow movement of randomly biased random walk $(X_n)$ on a supercritical Galton--Watson tree, and are interested in the sites on the tree that are most visited by the biased random walk. Our main result implies tightness of the distributions of the most visited sites under the annealed measure. This is in contrast with the one-dimensional case, and provides, to the best of our knowledge, the first non-trivial example of null recurrent random walk whose most visited sites are not transient, a question originally raised by Erd\\H{o}s and R\\'ev\\'esz [11] for simple symmetric random walk on the line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-10T09:57:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G50",
      "60K37"
    ],
    "keywords": [
      "biased random walk",
      "visited sites",
      "simple symmetric random walk",
      "null recurrent random walk",
      "main result implies tightness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}