{
  "id": "0901.4393",
  "version": "v1",
  "published": "2009-01-28T02:42:21.000Z",
  "updated": "2009-01-28T02:42:21.000Z",
  "title": "Excited against the tide: A random walk with competing drifts",
  "authors": [
    "Mark Holmes"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a random walk that has a drift $\\frac{\\beta}{d}$ to the right when located at a previously unvisited vertex and a drift $\\frac{\\mu}{d}$ to the left otherwise. We prove that in high dimensions, for every $\\mu$, the drift to the right is a strictly increasing and continuous function of $\\beta$, and that there is precisely one value $\\beta_0(\\mu,d)$ for which the resulting speed is zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-28T02:42:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B41"
    ],
    "keywords": [
      "random walk",
      "competing drifts",
      "high dimensions",
      "continuous function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.4393H"
    }
  }
}