文章基本信息

标题：Metrics on sets of interval partitions with diversity
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作者：Noah Forman ; Soumik Pal ; Douglas Rizzolo 等
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2020
卷号：25
DOI：10.1214/20-ECP317
语种：English
出版社：Electronic Communications in Probability
摘要：We first consider interval partitions whose complements are Lebesgue-null and introduce a complete metric that induces the same topology as the Hausdorff distance (between complements). This is done using correspondences between intervals. Further restricting to interval partitions with $\alpha $-diversity, we then adjust the metric to incorporate diversities. We show that this second metric space is Lusin. An important feature of this topology is that path-continuity in this topology implies the continuous evolution of diversities. This is important in related work on tree-valued stochastic processes where diversities are branch lengths.
关键词：interval partition; Poisson–Dirichlet distribution; $\alpha $-diversity