{
  "id": "1912.06503",
  "version": "v1",
  "published": "2019-12-13T14:08:35.000Z",
  "updated": "2019-12-13T14:08:35.000Z",
  "title": "Almost Sure Central Limit Theorems in Stochastic Geometry",
  "authors": [
    "Giovanni-Luca Torrisi",
    "Emilio Leonardi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total edge length of the $k$-nearest neighbors random graph, $(ii)$ the clique count in random geometric graphs, $(iii)$ the volume of the set approximation via the Poisson-Voronoi tessellation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-13T14:08:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G55",
      "60H07",
      "60D05"
    ],
    "keywords": [
      "sure central limit theorem",
      "stochastic geometry",
      "nearest neighbors random graph",
      "total edge length",
      "random geometric graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}