{
  "id": "0805.0729",
  "version": "v2",
  "published": "2008-05-06T14:41:30.000Z",
  "updated": "2008-07-17T09:19:09.000Z",
  "title": "Random walk weakly attracted to a wall",
  "authors": [
    "Joël De Coninck",
    "François Dunlop",
    "Thierry Huillet"
  ],
  "comment": "Replacement with minor changes and additions in bibliography. Same abstract, in plain text rather than TeX",
  "doi": "10.1007/s10955-008-9609-9",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a random walk X_n in Z_+, starting at X_0=x>= 0, with transition probabilities P(X_{n+1}=X_n+1|X_n=y>=1)=1/2-\\delta/(4y+2\\delta) P(X_{n+1}=X_n+1|X_n=y>=1)=1/2+\\delta/(4y+2\\delta) and X_{n+1}=1 whenever X_n=0. We prove that the expectation value of X_n behaves like n^{1-(\\delta/2)} as n goes to infinity when \\delta is in the range (1,2). The proof is based upon the Karlin-McGregor spectral representation, which is made explicit for this random walk.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-17T09:19:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "82B41",
      "42C05"
    ],
    "keywords": [
      "random walk",
      "karlin-mcgregor spectral representation",
      "transition probabilities",
      "expectation value"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2008,
      "month": "Oct",
      "volume": 133,
      "number": 2,
      "pages": 271
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JSP...133..271D"
    }
  }
}