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LIMIT THEORY FOR RANDOM SEQUENTIAL PACKING AND DEPOSITION

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By Mathew D. Penrose and J.E. Yukich

Consider sequential packing of unit balls in a large cube, as in
the Renyi car-parking model, but in any dimension and with
finite input. We prove a law of large numbers and central limit
theorem for the number of packed balls in the thermodynamic limit.
We prove analogous results for numerous related applied models,
including cooperative sequential adsorption, ballistic
deposition, and spatial birth-growth models.
The proofs are based on a general law of large numbers and
central limit theorem for ``stabilizing'' functionals of marked
point processes of independent uniform points in a large cube,
which are of independent interest. ``Stabilization'' means,
loosely, that local modifications have only local effects.