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Gaussian Limits for Multidimensional Random Sequential Packing at Saturation |
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| Authors: | T. Schreiber Mathew D. Penrose J. E. Yukich |
| Affiliation: | (1) Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland;(2) Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom;(3) Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA |
| 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 → ∞. 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. Research partially supported by the Polish Minister of Scientific Research and Information Technology grant 1 P03A 018 28 (2005-2007) Research supported in part by NSF grant DMS-0203720 |
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