{
  "id": "2209.12098",
  "version": "v1",
  "published": "2022-09-24T22:31:08.000Z",
  "updated": "2022-09-24T22:31:08.000Z",
  "title": "Lower bounds for the directional discrepancy with respect to an interval of rotations",
  "authors": [
    "Dmitriy Bilyk",
    "Michelle Mastrianni"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in $\\mathbb{R}^2$ rotated in a restricted interval of directions $[-\\theta, \\theta]$ with $\\theta < \\frac{\\pi}{4}$ is of the order at least $N^{1/5}$ with a constant depending on $\\theta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-24T22:31:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "optimal directional discrepancy",
      "rectangles",
      "restricted interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}