{
  "id": "1008.4321",
  "version": "v2",
  "published": "2010-08-25T17:42:39.000Z",
  "updated": "2011-06-17T22:22:38.000Z",
  "title": "The self-avoiding walk in a strip",
  "authors": [
    "Ben Dyhr",
    "Michael Gilbert",
    "Tom Kennedy",
    "Gregory F. Lawler",
    "Shane Passon"
  ],
  "comment": "30 pages, 3 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We review the existence of the infinite length self-avoiding walk in the half plane and its relationship to bridges. We prove that this probability measure is also given by the limit as $\\beta \\rightarrow \\beta_c-$ of the probability measure on all finite length walks $\\omega$ with the probability of $\\omega$ proportional to $\\beta_c^{|\\omega|}$ where $|\\omega|$ is the number of steps in $\\omega$. The self-avoiding walk in a strip $\\{z : 0<\\Im(z)<y\\}$ is defined by considering all self-avoiding walks $\\omega$ in the strip which start at the origin and end somewhere on the top boundary with probability proportional to $\\beta_c^{|\\omega|}$ We prove that this probability measure may be obtained by conditioning the SAW in the half plane to have a bridge at height $y$. This observation is the basis for simulations to test conjectures on the distribution of the endpoint of the SAW in a strip and the relationship between the distribution of this strip SAW and SLE$_{8/3}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-17T22:22:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B41"
    ],
    "keywords": [
      "probability measure",
      "half plane",
      "finite length walks",
      "infinite length self-avoiding walk",
      "relationship"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-011-0258-z",
      "journal": "Journal of Statistical Physics",
      "year": 2011,
      "month": "Jul",
      "volume": 144,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JSP...144....1D"
    }
  }
}