Limits of logarithmic combinatorial, structures

• 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 PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2000
• 页码: 1620-1644
• 关键词: NUMBER; distributions; CONVERGENCE; components; THEOREM

摘要

Under very mild conditions, we prove that the limiting behavior of the component counts in a decomposable logarithmic combinatorial structure conforms to a single, unified pattern, which includes functional central limit theorems, Erdas-Turan laws, Poisson-Dirichlet limits for the large components and Poisson approximation in total variation for the total number of components. Our approach is entirely probabilistic, and the conditions can readily be verified in practice.