{
  "id": "0706.4395",
  "version": "v2",
  "published": "2007-06-29T12:25:17.000Z",
  "updated": "2008-03-31T19:19:40.000Z",
  "title": "The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems",
  "authors": [
    "Jens Marklof",
    "Andreas Strömbergsson"
  ],
  "comment": "Corrected typos, added an index of notation",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP",
    "math.NT"
  ],
  "abstract": "The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we investigate the Boltzmann-Grad limit, where the radius of each scatterer tends to zero, and prove the existence of a limiting distribution for the free path length of the periodic Lorentz gas. We also discuss related problems, such as the statistical distribution of directions of lattice points that are visible from a fixed position.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-31T19:19:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A60",
      "37D50",
      "82C05",
      "82C40",
      "11P21"
    ],
    "keywords": [
      "periodic lorentz gas",
      "related lattice point problems",
      "free path length",
      "distribution",
      "chaotic diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.4395M"
    }
  }
}