{
  "id": "0901.0699",
  "version": "v3",
  "published": "2009-01-06T19:42:05.000Z",
  "updated": "2009-11-19T14:55:43.000Z",
  "title": "New bounds for the free energy of directed polymers in dimension 1+1 and 1+2",
  "authors": [
    "Hubert Lacoin"
  ],
  "comment": "31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physics",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-19T14:55:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82D60",
      "60K37",
      "82B44"
    ],
    "keywords": [
      "free energy",
      "directed polymer",
      "strong disorder holds",
      "random environment",
      "high temperature"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-009-0957-3",
      "journal": "Communications in Mathematical Physics",
      "year": 2010,
      "month": "Mar",
      "volume": 294,
      "number": 2,
      "pages": 471
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.294..471L"
    }
  }
}