{
  "id": "1510.06287",
  "version": "v1",
  "published": "2015-10-21T15:00:24.000Z",
  "updated": "2015-10-21T15:00:24.000Z",
  "title": "Universality in marginally relevant disordered systems",
  "authors": [
    "Francesco Caravenna",
    "Rongfeng Sun",
    "Nikos Zygouras"
  ],
  "comment": "47 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider disordered systems of directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2+1), the long-range directed polymer model with Cauchy tails in dimension (1+1) and the disordered pinning model with tail exponent 1/2. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field with a multi-scale correlation structure, which undergoes a phase transition as the disorder strength varies. As a by-product, we show that the solution of the two-dimensional Stochastic Heat Equation, suitably regularized, converges to the same limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T15:00:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D60",
      "60K35"
    ],
    "keywords": [
      "marginally relevant disordered systems",
      "universality",
      "two-dimensional stochastic heat equation",
      "long-range directed polymer model",
      "log-normal random field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006287C"
    }
  }
}