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Gaussian limits for multidimensional random sequential packing at saturation (extended version)

T. Schreiber·Mathew D. Penrose·J. E. Yukich
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Abstract

Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $λ$ is asymptotically normal as $λ\to \infty$. We provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized Gaussian field. The method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization.

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T. Schreiber, Mathew D. Penrose, J. E. Yukich. 2006-10-23. Gaussian limits for multidimensional random sequential packing at saturation (extended version). https://doi.org/10.1007/s00220-007-0218-2

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