{
  "id": "math/0507054",
  "version": "v1",
  "published": "2005-07-04T08:56:29.000Z",
  "updated": "2005-07-04T08:56:29.000Z",
  "title": "Random walk attracted by percolation clusters",
  "authors": [
    "Serguei Popov",
    "Marina Vachkovskaia"
  ],
  "comment": "13 pages",
  "journal": "Electronic Communications in Probability, v. 10, n. 27, p. 263-272, 2005",
  "categories": [
    "math.PR"
  ],
  "abstract": "Starting with a percolation model in $\\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$. This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For $f(t)=e^{\\beta t}$ we prove that there is a phase transition in $\\beta$, i.e., the random walk is subdiffusive for large $\\beta$ and is diffusive for small $\\beta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-04T08:56:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60J10"
    ],
    "keywords": [
      "random walk",
      "percolation clusters",
      "phase transition",
      "bigger clusters",
      "percolation model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7054P"
    }
  }
}