{
  "id": "0910.0069",
  "version": "v7",
  "published": "2009-10-01T10:30:24.000Z",
  "updated": "2012-03-28T08:28:02.000Z",
  "title": "Directed polymers and the quantum Toda lattice",
  "authors": [
    "Neil O'Connell"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP632 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2012, Vol. 40, No. 2, 437-458",
  "doi": "10.1214/10-AOP632",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2012-03-28T08:28:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum toda lattice",
      "yor concerning exponential functionals",
      "brownian directed polymer model",
      "diffusion process",
      "multidimensional generalization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0069O"
    }
  }
}