{
  "id": "1312.3357",
  "version": "v3",
  "published": "2013-12-11T21:55:11.000Z",
  "updated": "2016-10-24T21:54:01.000Z",
  "title": "Polynomial chaos and scaling limits of disordered systems",
  "authors": [
    "Francesco Caravenna",
    "Rongfeng Sun",
    "Nikos Zygouras"
  ],
  "comment": "55 pages. Final version. To appear in JEMS",
  "categories": [
    "math.PR"
  ],
  "abstract": "Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable, given by a Wiener chaos expansion over the d-dimensional white noise. A key ingredient in our approach is a Lindeberg principle for polynomial chaos expansions, which extends earlier work of Mossel, O'Donnell and Oleszkiewicz. These results provide a unified framework to study the continuum and weak disorder scaling limits of statistical mechanics systems that are disorder relevant, including the disordered pinning model, the (long-range) directed polymer model in dimension 1+1, and the two-dimensional random field Ising model. This gives a new perspective in the study of disorder relevance, and leads to interesting new continuum models that warrant further studies.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-12T19:16:15.000Z",
      "comment": "55 pages. Revised version. To appear in JEMS",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-10-24T21:54:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D60",
      "60K35"
    ],
    "keywords": [
      "scaling limits",
      "disordered systems",
      "polynomial chaos expansions",
      "two-dimensional random field ising model",
      "wiener chaos expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3357C"
    }
  }
}