{
  "id": "0811.2806",
  "version": "v2",
  "published": "2008-11-17T21:15:50.000Z",
  "updated": "2009-05-18T20:15:22.000Z",
  "title": "Logarithm laws for unipotent flows, I",
  "authors": [
    "Jayadev S. Athreya",
    "Grigorii Margulis"
  ],
  "comment": "submitted to the Journal of Modern Dynamics; revised version, paper is now split into two pieces, this first half contains results on the space of lattices, the second part will contain results on general homogeneous spaces",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We prove analogues of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we obtain results for one-parameter actions on the space of lattices $SL(n, \\R)/SL(n, \\Z)$. The key lemma for our results says the measure of the set of unimodular lattices in $\\R^n$ that does not intersect a `large' volume subset of $\\R^n$ is `small'. This can be considered as a `random' analogue of the classical Minkowski theorem in the geometry of numbers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-18T20:15:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H16"
    ],
    "keywords": [
      "unipotent flows",
      "logarithm laws",
      "one-parameter actions",
      "results says",
      "unimodular lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.2806A"
    }
  }
}