Exact and approximate results for deposition and annihilation processes on graphs

• 成果类型: Article
• 署名作者: Penrose, MD; Sudbury, A
• 署名单位: University of Bath; Monash University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000765
• 发表日期: 2005
• 页码: 853-889
• 关键词: random sequential adsorption; hard-core; limit; coverage; lattice; MODEL; line

摘要

We consider random sequential adsorption processes where the initially empty sites of a graph are irreversibly occupied, in random order, either by monomers which block neighboring sites, or by dimers. We also consider a process where initially occupied sites annihilate their neighbors at random times. We verify that these processes are well defined on infinite graphs, and derive forward equations governing joint vacancy/occupation probabilities. Using these, we derive exact formulae for occupation probabilities and pair correlations in Bethe lattices. For the blocking and annihilation processes we also prove positive correlations between sites an even distance apart, and for blocking we derive rigorous lower bounds for the site occupation probability in lattices, including a lower bound of 1/3 for Z(2). We also give normal approximation results for the number of occupied sites in a large finite graph.