Gaussian limits for multidimensional random sequential packing at saturation (extended version)
arXiv:math/0610680 · doi:10.1007/s00220-007-0218-2
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.
31 pages