{
  "id": "1505.04802",
  "version": "v1",
  "published": "2015-05-18T20:06:18.000Z",
  "updated": "2015-05-18T20:06:18.000Z",
  "title": "The crossing probability for directed polymers in random media",
  "authors": [
    "Andrea De Luca",
    "Pierre Le Doussal"
  ],
  "comment": "5 pages + 16 pages of supplemental material",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain analytical expressions for the first few moments of this probability, and compare them to a numerical simulation of a discrete model at high-temperature. From these observations, several large time properties of the non-crossing probabilities are conjectured. Extensions of our formalism to more general observables are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-18T20:06:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed polymers",
      "random media",
      "crossing probability",
      "large time properties",
      "replica method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}