{
  "id": "1902.04930",
  "version": "v1",
  "published": "2019-02-13T14:41:45.000Z",
  "updated": "2019-02-13T14:41:45.000Z",
  "title": "The scaling limits for Wiener sausages in random environments",
  "authors": [
    "Chien-Hao Huang"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the statistical mechanics of a random polymer with random walks and disorders in $\\mathbb{Z}^d$. The walk collects random disorders along the way and gets nothing if it visits the same site twice. In the continuum and weak disorder regime, the partition function as a random variable converges weakly to a Wiener Chaos expansion when the dimension is lower than the critical dimension, which is four. A finite temperature case in one dimension is also discussed. The last case suggests that the end-point behavior of the polymer is $t^{2/3}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T14:41:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60Fxx",
      "82D30"
    ],
    "keywords": [
      "wiener sausages",
      "random environments",
      "scaling limits",
      "walk collects random disorders",
      "finite temperature case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}