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标题：On the block counting process and the fixation line of exchangeable coalescents
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作者：Florian Gaiser ; Martin Möhle
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
期号：2
页码：809-833
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study the block counting process and the fixation line of exchangeablecoalescents. Formulas for the infinitesimal rates of both processes are provided.It is shown that the block counting process is Siegmund dual to the fixation line.For exchangeable coalescents restricted to a sample of size n and with dust weprovide a convergence result for the block counting process as n tends to infinity.The associated limiting process is related to the frequencies of singletons ofthe coalescent. Via duality we obtain an analog convergence result for the fixationline of exchangeable coalescents with dust. The Dirichlet coalescent and thePoisson–Dirichlet coalescent are studied in detail.
关键词：Block counting process; coming down from infinity; Dirichlet coales-;cent; duality; dust; exchangeable coalescent; fixation line; Poisson–Dirichlet coalescent.