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.
Publié le : 2002-02-14
Classification:
Packing,
sequential adsorption,
ballistic deposition,
spatial birth-growth models,
epidemic growth,
desorption,
law of large numbers,
central limit theorem,
82C21,
60F05,
60F15,
60G55
@article{1015961164,
author = {Penrose, Mathew D. and Yukich, J.E.},
title = {Limit Theory for Random Sequential Packing and Deposition},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 272-301},
language = {en},
url = {http://dml.mathdoc.fr/item/1015961164}
}
Penrose, Mathew D.; Yukich, J.E. Limit Theory for Random Sequential Packing and Deposition. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 272-301. http://gdmltest.u-ga.fr/item/1015961164/