{
  "id": "1705.08735",
  "version": "v1",
  "published": "2017-05-24T12:58:45.000Z",
  "updated": "2017-05-24T12:58:45.000Z",
  "title": "Weighted Poisson-Delaunay Mosaics",
  "authors": [
    "Herbert Edelsbrunner",
    "Anton Nikitenko"
  ],
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "Slicing a Voronoi tessellation in $\\mathbb{R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in $\\mathbb{R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-24T12:58:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "68U05",
      "I.3.5",
      "G.3",
      "G.2"
    ],
    "keywords": [
      "weighted poisson-delaunay mosaics",
      "smallest empty circumscribed sphere",
      "dual weighted delaunay mosaic",
      "generalized discrete morse function",
      "dimensional weighted voronoi tessellation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}