{
  "id": "0907.3805",
  "version": "v1",
  "published": "2009-07-22T09:35:34.000Z",
  "updated": "2009-07-22T09:35:34.000Z",
  "title": "The linking number and the writhe of uniform random walks and polygons in confined spaces",
  "authors": [
    "E. Panagiotou",
    "K. C. Millett",
    "S. Lambropoulou"
  ],
  "comment": "29 pages, 12 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. We show that the mean squared linking number, the mean squared writhe and the mean squared self-linking number of oriented uniform random walks or polygons of length $n$, in a convex confined space, are of the form $O(n^2)$. Moreover, for a fixed simple closed curve in a convex confined space, we prove that the mean absolute value of the linking number between this curve and a uniform random walk or polygon of $n$ edges is of the form $O(\\sqrt{n})$. Our numerical studies confirm those results. They also indicate that the mean absolute linking number between any two oriented uniform random walks or polygons, of $n$ edges each, is of the form O(n). Equilateral random walks and polygons are used to model polymers in $\\theta$-conditions. We use numerical simulations to investigate how the self-linking and linking number of equilateral random walks scale with their length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-22T09:35:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "82D60",
      "92C40"
    ],
    "keywords": [
      "linking number",
      "oriented uniform random walks",
      "convex confined space",
      "model polymers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/43/4/045208",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Jan",
      "volume": 43,
      "number": 4,
      "pages": "045208"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43d5208P"
    }
  }
}