{
  "id": "math/0107055",
  "version": "v2",
  "published": "2001-07-06T20:32:49.000Z",
  "updated": "2002-06-28T21:24:42.000Z",
  "title": "Markov Chain Intersections and the Loop-Erased Walk",
  "authors": [
    "Russell Lyons",
    "Yuval Peres",
    "Oded Schramm"
  ],
  "comment": "To appear in Ann. Inst. H. Poincar\\'e Probab. Statist",
  "journal": "Ann.Inst.H.PoincareProbab.Statist.39:779-791,2003",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let X and Y be independent transient Markov chains on the same state space that have the same transition probabilities. Let L denote the ``loop-erased path'' obtained from the path of X by erasing cycles when they are created. We prove that if the paths of X and Y have infinitely many intersections a.s., then L and Y also have infinitely many intersections a.s.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-06-28T21:24:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60G17"
    ],
    "keywords": [
      "markov chain intersections",
      "loop-erased walk",
      "independent transient markov chains",
      "state space",
      "transition probabilities"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/S0246-0203(03)00033-5"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 580929,
      "adsabs": "2003AnIHP..39..779L"
    }
  }
}