{
  "id": "1211.2987",
  "version": "v1",
  "published": "2012-11-13T13:28:31.000Z",
  "updated": "2012-11-13T13:28:31.000Z",
  "title": "Random walk in mixed random environment without uniform ellipticity",
  "authors": [
    "Ostap Hryniv",
    "Mikhail V. Menshikov",
    "Andrew R. Wade"
  ],
  "comment": "20 pages",
  "journal": "Proceedings of the Steklov Institute of Mathematics, Vol. 282 (2013), no. 1, p. 106-123",
  "doi": "10.1134/S0081543813060102",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i) points endowed with probabilities drawn from a symmetric distribution with heavy tails at 0 and 1, and (ii) `fast points' with a fixed systematic drift. Without these fast points, the model is related to the diffusion in heavy-tailed (`stable') random potential studied by Schumacher and Singh; the fast points perturb that model. The two components compete to determine the behaviour of the random walk; we identify phase transitions in terms of the model parameters. We give conditions for recurrence and transience, and prove almost-sure bounds for the trajectories of the walk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-13T13:28:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60J10",
      "60F15"
    ],
    "keywords": [
      "random walk",
      "mixed random environment",
      "uniform ellipticity",
      "fast points perturb",
      "almost-sure bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2987H"
    }
  }
}