{
  "id": "cond-mat/0211141",
  "version": "v2",
  "published": "2002-11-07T19:25:10.000Z",
  "updated": "2002-11-08T09:22:40.000Z",
  "title": "Dynamical Windings of Random Walks and Exclusion Models. Part I: Thermodynamic Limit",
  "authors": [
    "Guy Fayolle",
    "Cyril Furtlehner"
  ],
  "comment": "31 pages, 13 figures. Pages 5,6,8,9,10,12,23 color printed. INRIA Report 4608",
  "journal": "J. Stat. Phys. Vol. 114, No 1-2 (2004), 229-260",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR"
  ],
  "abstract": "We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\\eta$ which breaks the symmetry between the left and right orientation, the winding distribution of the walk is modified, and the system can be in three different phases: folded, stretched and glassy. An explicit mapping is found, leading to consider the system as a coupling of two exclusion processes. For all closed or periodic initial sample paths, a convenient scaling permits to show a convergence in law (or almost surely on a modified probability space) to a continuous curve, the equation of which is given by a system of two non linear stochastic differential equations. The deterministic part of this system is explicitly analyzed via elliptic functions. In a similar way, by using a formal fluid limit approach, the dynamics of the system is shown to be equivalent to a system of two coupled Burgers' equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-08T09:22:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walk",
      "thermodynamic limit",
      "exclusion models",
      "dynamical windings",
      "non linear stochastic differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}