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arXiv · 1910.01732

Site Frequency Spectrum of the Bolthausen-Sznitman Coalescent

Götz Kersting·Arno Siri-Jégousse·Alejandro H. Wences
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Abstract

We derive explicit formulas for the two first moments of he site frequency spectrum $(SFS_{n,b})_{1\leq b\leq n-1}$ of the Bolthausen-Sznitman coalescent along with some precise and efficient approximations, even for small sample sizes $n$. These results provide new $L_2$-asymptotics for some values of $b=o(n)$. We also study the length of internal branches carrying $b>n/2$ individuals. In this case we obtain the distribution function and a convergence in law. Our results rely on the random recursive tree construction of the Bolthausen-Sznitman coalescent.

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Götz Kersting, Arno Siri-Jégousse, Alejandro H. Wences. 2019-10-03. Site Frequency Spectrum of the Bolthausen-Sznitman Coalescent. https://arxiv.org/abs/1910.01732

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