### 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.

Original language | English |
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Article number | 91 |

Pages (from-to) | 2509-2544 |

Number of pages | 36 |

Journal | Electronic Journal of Probability |

Volume | 16 |

Publication status | Published - 2011 |

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## Cite this

Penrose, M. D., & Peres, Y. (2011). Local central limit theorems in stochastic geometry.

*Electronic Journal of Probability*,*16*, 2509-2544. [91].