The Annals of Applied Probability

Limit Theory for Random Sequential Packing and Deposition

Mathew D. Penrose and J.E. Yukich

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Consider sequential packing of unit balls in a large cube, as in the Rényi 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.

Article information

Ann. Appl. Probab., Volume 12, Number 1 (2002), 272-301.

First available in Project Euclid: 12 March 2002

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Zentralblatt MATH identifier

Primary: 82C21: Dynamic continuum models (systems of particles, etc.)
Secondary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 60G55: Point processes

Packing sequential adsorption ballistic deposition spatial birth-growth models epidemic growth desorption law of large numbers central limit theorem


Penrose, Mathew D.; Yukich, J.E. Limit Theory for Random Sequential Packing and Deposition. Ann. Appl. Probab. 12 (2002), no. 1, 272--301. doi:10.1214/aoap/1015961164.

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