arXiv Open Access 2023

On a Markov chain related to the individual lengths in the recursive construction of Kingman's coalescent

Linglong Yuan
Lihat Sumber

Abstrak

Kingman's coalescent is a widely used process to model sample genealogies in population genetics. Recently there have been studies on the inference of quantities related to the genealogy of additional individuals given a known sample. This paper explores the recursive (or sequential) construction which is a natural way of enlarging the sample size by adding individuals one after another to the sample genealogy via individual lineages to construct the Kingman's coalescent. Although the process of successively added lineage lengths is not Markovian, we show that it contains a Markov chain which records the information of the successive largest lineage lengths and we prove a limit theorem for this Markov chain.

Topik & Kata Kunci

Penulis (1)

L

Linglong Yuan

Format Sitasi

Yuan, L. (2023). On a Markov chain related to the individual lengths in the recursive construction of Kingman's coalescent. https://arxiv.org/abs/2310.14882

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2023
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓