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arXiv · 1908.01474

Integral representation of probabilities in Kingman coalescent

Youzhou Zhou
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Abstract

Kingman Coalescent was first proposed by Kingman [7] in population genetics to describe population's genealogical structure. Now it becomes a bench-mark model for coalescent process. Extensive studies have been conducted on Kingman coalescent. In particular, its explicit finite time distribution was obtained by Tavar\'e [12]. However, very few people use this explicit distribution to do analysis for it is an intractable infinite series. In this article, we are going to establish a complex integral representation for the finite time distribution, then we use steepest descent method to analyze this integral representation to obtain local central limit theorem at small time regime.

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Youzhou Zhou. 2019-08-05. Integral representation of probabilities in Kingman coalescent. https://arxiv.org/abs/1908.01474

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