{
  "id": "1410.7090",
  "version": "v1",
  "published": "2014-10-26T22:06:22.000Z",
  "updated": "2014-10-26T22:06:22.000Z",
  "title": "Excursions and occupation times of critical excited random walks",
  "authors": [
    "Dmitry Dolgopyat",
    "Elena Kosygina"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper considers excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on the critical case for the transition between recurrence and transience which occurs when the total expected drift $\\delta$ at each site of the environment is equal to 1 in absolute value. Several crucial estimates for ERWs fail in the critical case and require a separate treatment. The main results discuss the depth and duration of excursions from the origin for$|\\delta|=1$ as well as occupation times of negative and positive semi-axes and scaling limits of ERW indexed by these occupation times. It is also pointed out that the limiting proportions of the time spent by a non-critical recurrent ERW (i.e. when $|\\delta|<1$) above or below zero converge to beta random variables with explicit parameters given in terms of $\\delta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-26T22:06:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F17",
      "60J80",
      "60J60"
    ],
    "keywords": [
      "critical excited random walks",
      "occupation times",
      "excursions",
      "critical case",
      "beta random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7090D"
    }
  }
}