The number of components in a logarithmic combinatorial structure

• 成果类型: Article
• 署名作者: Arratia, R; Barbour, AD; Tavaré, S
• 署名单位: University of Southern California; University of Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2000
• 页码: 331-361
• 关键词: independent process approximations; total variation asymptotics; limit-theorem; distributions; allocation; particles; cells

摘要

Under very mild conditions, we prove that the number of components in a decomposable logarithmic combinatorial structure has a distribution which is close to Poisson in total variation. The conditions are satisfied for all assemblies, multisets and selections in the logarithmic class. The error in the Poisson approximation is shown under marginally more restrictive conditions to be of exact order O(1/ log n), by exhibiting the penultimate asymptotic approximation; similar results have previously been obtained by Hwang [20], under stronger assumptions. Our method is entirely probabilistic, and the conditions can readily be verified in practice.