{
  "id": "2005.12706",
  "version": "v1",
  "published": "2020-05-26T13:27:17.000Z",
  "updated": "2020-05-26T13:27:17.000Z",
  "title": "Edwards-Wilkinson fluctuations for the directed polymer in the full $L^2$-regime for dimensions $d \\geq 3$",
  "authors": [
    "Dimitris Lygkonis",
    "Nikos Zygouras"
  ],
  "comment": "46 pages, 2 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $d\\geq 3$, if centered, scaled and averaged with respect to a test function $\\varphi \\in C_c(\\mathbb{R}^d)$, converges in distribution to a Gaussian random variable with explicit variance. Introducing a new idea of a martingale difference representation, we also prove that the log-partition function, which can be viewed as a discretisation of the KPZ equation, exhibits the same fluctuations, when centered and averaged with respect to a test function. Thus, the two models fall within the Edwards-Wilkinson universality class in the full $L^2$-regime, a result that was only established, so far, for a strict subset of this regime in $d\\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T13:27:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edwards-wilkinson fluctuations",
      "dimensions",
      "test function",
      "martingale difference representation",
      "edwards-wilkinson universality class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}