{
  "id": "2304.04871",
  "version": "v1",
  "published": "2023-04-10T21:32:15.000Z",
  "updated": "2023-04-10T21:32:15.000Z",
  "title": "Universality of directed polymers in the intermediate disorder regime",
  "authors": [
    "Julian Ransford"
  ],
  "comment": "40 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In 2018, Krishnan and Quastel showed that the fluctuations of Sepp\\\"al\\\"ainen's log-gamma polymer converge in law to the Tracy--Widom GUE distribution in the intermediate disorder regime, which corresponds to taking the inverse temperature $\\beta$ to depend on the length of the polymer $2n$, with $\\beta=n^{-\\alpha}$ for some $\\alpha<1/4$. They also conjectured that this should hold for directed polymers with general i.i.d weights. We prove that their conjecture is true for any $1/5<\\alpha<1/4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-10T21:32:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37"
    ],
    "keywords": [
      "intermediate disorder regime",
      "directed polymers",
      "universality",
      "tracy-widom gue distribution",
      "log-gamma polymer converge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}