Local central limit theorems in stochastic geometry

Details Local central limit theorems in stochastic geometry Local central limit theorems in stochastic geometry

2010-06-17

arxiv.org/abs/1006.3523v2

Mathematics

Probability

V1: 31 pages. V2: 45 pages, with new results added in Section 5 and extra explanation added elsewhere

Scientific paper

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.

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