Asymptotics of the Minimal Clade Size and Related Functionals of Certain Beta-Coalescents

Siri-Jegousse, Arno and Yuan, Linglong ORCID: 0000-0002-7851-1631 (2016) Asymptotics of the Minimal Clade Size and Related Functionals of Certain Beta-Coalescents. Acta Applicandae Mathematicae, 142 (1). pp. 127-148.

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Abstract

The Beta(2−α,α) n-coalescent with 1<α<2 is a Markov process taking values in the set of partitions of {1,…,n}. It evolves from the initial value {1},…,{n} by merging (coalescing) blocks together into one and finally reaching the absorbing state {1,…,n}. This article aims to give the asymptotic distribution of the size of the minimal clade of 1, which is the block containing 1 at the time of coalescence of the singleton {1}. To this, we express it as a function of the coalescence time of {1}, the number of blocks involved and their sizes. The asymptotic behaviours of those related functionals are therefore also studied.

Item Type:	Article
Uncontrolled Keywords:	Beta-coalescent, Ranked Lambda-coalescent, Kingman's paintbox construction, Minimal clade size, External branch lengths, Block-counting process
Depositing User:	Symplectic Admin
Date Deposited:	01 Apr 2020 10:36
Last Modified:	18 Jan 2023 23:56
DOI:	10.1007/s10440-015-0020-7
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3081345