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February 2002 Limit Theory for Random Sequential Packing and Deposition
Mathew D. Penrose, J.E. Yukich
Ann. Appl. Probab. 12(1): 272-301 (February 2002). DOI: 10.1214/aoap/1015961164


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.


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Mathew D. Penrose. J.E. Yukich. "Limit Theory for Random Sequential Packing and Deposition." Ann. Appl. Probab. 12 (1) 272 - 301, February 2002.


Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1018.60023
MathSciNet: MR1890065
Digital Object Identifier: 10.1214/aoap/1015961164

Primary: 82C21
Secondary: 60F05 , 60F15 , 60G55

Keywords: ballistic deposition , central limit theorem , desorption , epidemic growth , Law of Large Numbers , Packing , sequential adsorption , spatial birth-growth models

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 1 • February 2002
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