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: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3081345 |
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