The Annals of Applied Probability

Limit Theory for Random Sequential Packing and Deposition

Mathew D. Penrose and J.E. Yukich

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015961164

Digital Object Identifier
doi:10.1214/aoap/1015961164

Mathematical Reviews number (MathSciNet)
MR1890065

Zentralblatt MATH identifier
1018.60023

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1015961164


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  • BETHLEHEM, PENNSYLVANIA 18015 USA E-MAIL: joseph.yukich@lehigh.edu