{
  "id": "1006.3523",
  "version": "v2",
  "published": "2010-06-17T17:13:19.000Z",
  "updated": "2011-08-15T12:09:47.000Z",
  "title": "Local central limit theorems in stochastic geometry",
  "authors": [
    "Mathew D. Penrose",
    "Yuval Peres"
  ],
  "comment": "V1: 31 pages. V2: 45 pages, with new results added in Section 5 and extra explanation added elsewhere",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-15T12:09:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60D05",
      "60K35",
      "05C80"
    ],
    "keywords": [
      "stochastic geometry",
      "general local central limit theorem",
      "finite-input random sequential adsorption",
      "independent random variables",
      "random geometric graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.3523P"
    }
  }
}