Limit theory for random sequential packing and deposition

• 成果类型: Article
• 署名作者: Penrose, MD; Yukich, JE
• 署名单位: Durham University; Lehigh University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 272-301
• 关键词: ballistic deposition; adsorption; particles; kinetics; parking; models

摘要

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.