与Bolthausen-Sznitman聚结相关的等位基因频率谱的渐近性
Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent
摘要：
我们在无限多等位基因模型的背景下工作。与从n个个体开始的合并过程相关的等位基因分区是通过沿着合并树的骨架放置突变来获得的;对于每个个体，我们追溯到影响它的最近突变，并将最近突变相同的个体分组在一起。该分区中的每个不同可能大小的块的数量是等位基因频谱。著名的Ewens抽样公式给出了与Kingman聚结相关的等位基因频谱的精确概率。这（和退化的星形聚结）是唯一的明确的概率已知的λ聚结，虽然他们是已知的，以满足递归由于Moehle。最近，Berestycki，Berestycki和Schweinsberg证明了β（2-α，α）与α在（1，2）中结合的等位基因频谱的渐近结果。在本文中，我们证明了完全渐近的情况下，Bolthausen-Sznitman合并。
英文摘要：
We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each individual, we trace back to the most recent mutation affecting it and group together individuals whose most recent mutations are the same. The number of blocks of each of the different possible sizes in this partition is the allele frequency spectrum. The celebrated Ewens sampling formula gives precise probabilities for the allele frequency spectrum associated with Kingman's coalescent. This (and the degenerate star-shaped coalescent) are the only Lambda coalescents for which explicit probabilities are known, although they are known to satisfy a recursion due to Moehle. Recently, Berestycki, Berestycki and Schweinsberg have proved asymptotic results for the allele frequency spectra of the Beta(2-alpha,alpha) coalescents with alpha in (1,2). In this paper, we prove full asymptotics for the case of the Bolthausen-Sznitman coalescent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
