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Gaussian limits for multidimensional random sequential packing at saturation. (English) Zbl 1145.60017
Summary: 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 \(\lambda\) is asymptotically normal as \(\lambda \rightarrow \infty\). 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.

MSC:
60F05 Central limit and other weak theorems
60D05 Geometric probability and stochastic geometry
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