{
  "id": "2407.01633",
  "version": "v1",
  "published": "2024-06-29T20:54:53.000Z",
  "updated": "2024-06-29T20:54:53.000Z",
  "title": "A New Construction of Forests with Low Visibility",
  "authors": [
    "Kirill Kashkan"
  ],
  "categories": [
    "math.MG",
    "math.CO",
    "math.PR"
  ],
  "abstract": "A set of points with finite density is constructed in $\\mathbb{R}^d$, with $d\\geq2$, by adding points to a Poisson process such that any line segment of length $O\\left(\\varepsilon^{-(d-1)}\\ln\\varepsilon^{-1}\\right)$ in $\\mathbb{R}^d$ will contain one of the points of the set within distance $\\varepsilon$ of it. The constant implied by the big-$O$ notation depends on dimension only.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-29T20:54:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low visibility",
      "construction",
      "finite density",
      "poisson process",
      "line segment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}