Integral representation of probabilities in Kingman coalescent
| Autor: | Zhou, Youzhou |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 11 pages, 2 figures |
| Databáze: | arXiv |
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