{
  "annotation_id": "0d2271a7-20e1-448e-905b-a4e42ebbfb4f",
  "date_created": "2026-03-02T18:01:21.425000Z",
  "date_modified": "2026-03-02T18:01:21.425000Z",
  "file_hash": "634394e74daf793ccc1270f896e12b9910f660baf5fb497002fe7818f769a2be",
  "private": false,
  "record": {
    "abstract": "We consider the problem of finding, for a given quadratic measure of\nnon-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or\ndiaphony), the asymptotic distribution of this discrepancy for truly random\npoints in the limit $N\\to\\infty$. We then examine the circumstances under which\nthis distribution approaches a normal distribution. For large classes of\nnon-uniformity measures, a Law of Many Modes in the spirit of the Central Limit\nTheorem can be derived.",
    "arxiv_id": "physics/9708014",
    "authors": [
      "Andre van Hameren",
      "Ronald Kleiss",
      "Jiri Hoogland"
    ],
    "categories": [
      "physics.comp-ph",
      "hep-lat",
      "physics.data-an"
    ],
    "doi": "10.1016/S0010-4655(97)00105-7",
    "title": "Gaussian limits for discrepancies. I: Asymptotic results",
    "url": "https://arxiv.org/abs/physics/9708014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c3bab08b-9ec2-4b46-8739-d2f219cf3f80",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}