Local central limit theorems in stochastic geometry

Reference:

Penrose, M. D. and Peres, Y., 2011. Local central limit theorems in stochastic geometry. Electronic Journal of Probability, 16, 91.

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Official URL:

http://ejp.ejpecp.org/article/view/968/1155

Related URLs:

• http://ejp.ejpecp.org/article/view/968/1155

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.

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