# Some large deviations in Kingman's coalescent

@article{Depperschmidt2013SomeLD, title={Some large deviations in Kingman's coalescent}, author={Andrej Depperschmidt and Peter Pfaffelhuber and Annika Scheuringer}, journal={arXiv: Probability}, year={2013} }

Kingman's coalescent is a random tree that arises from classical population genetic models such as the Moran model. The individuals alive in these models correspond to the leaves in the tree and the following two laws of large numbers concerning the structure of the tree-top are well-known: (i) The (shortest) distance, denoted by $T_n$, from the tree-top to the level when there are $n$ lines in the tree satisfies $nT_n \xrightarrow{n\to\infty} 2$ almost surely; (ii) At time $T_n$, the…

## 6 Citations

Integral representation of probabilities in Kingman coalescent

- Mathematics
- 2019

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…

Large deviations for homozygosity

- Mathematics
- 2016

For any $m \geq 2$, the homozygosity of order $m$ of a population is the probability that a sample of size $m$ from the population consists of the same type individuals. Assume that the type…

The Kingman tree length process has infinite quadratic variation

- Mathematics
- 2014

In the case of neutral populations of fixed sizes in equilibrium whose genealogies are described by the Kingman N-coalescent back from time t consider the associated processes of total tree length as…

Integral representation for Kingman coalescent

- MathematicsSCIENTIA SINICA Mathematica
- 2020

Kingman coalescent is the (cid:12)rst coalescent model. It has become a benchmark coalescent model recently, and has been widely studied. This article aims at establishing an alternative integral…

Asymptotic expansions and precise deviations in the Kingman coalescent

- Mathematics
- 2021

In this paper, we study the small-time asymptotic behavior of the Kingman coalescent. We obtain the Berry-Esseen bound and the Edgeworth expansion in the central limit theorem. Moreover, by the…

Limit theorems for pure death processes coming down from infinity

- MathematicsJournal of Applied Probability
- 2017

A pure death process coming down from infinity as a natural generalization of the death process associated with the Kingman coalescent is treated and a number of limit theorems including a strong law of large numbers and a large deviation theorem are established.

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