{
  "id": "2010.03609",
  "version": "v1",
  "published": "2020-10-07T19:06:45.000Z",
  "updated": "2020-10-07T19:06:45.000Z",
  "title": "The Manhattan and Lorentz Mirror Models -- A result on the Cylinder with low density of mirrors",
  "authors": [
    "Kieran Ryan"
  ],
  "comment": "13 pages, 7 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the Manhattan and Lorentz Mirror models on an infinite cylinder of finite even width $n$, with the mirror probability $p$ satisfying $p<Cn^{-1}$, $C$ a constant. We use the Brauer and Walled Brauer algebras to show that the maximum height along the cylinder reached by a walker is order $p^{-2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-07T19:06:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B41"
    ],
    "keywords": [
      "lorentz mirror models",
      "low density",
      "infinite cylinder",
      "mirror probability",
      "walled brauer algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}