A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents



Siri-Jégousse, Arno and Yuan, Linglong ORCID: 0000-0002-7851-1631
(2018) A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents. In: XII Symposium of Probability and Stochastic Processes. Progress in Probability, 73 . Springer International Publishing, pp. 219-234. ISBN 9783319776422

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Abstract

We study the largest block size of Beta n-coalescents at small times as n tends to infinity, using the paintbox construction of Beta-coalescents and the link between continuous-state branching processes and Beta-coalescents established in Birkner et al. (Electron J Probab 10(9):303–325, 2005) and Berestycki et al. (Ann Inst H Poincaré Probab Stat 44(2):214–238, 2008). As a corollary, a limit result on the largest block size at the coalescence time of the individual/block {1} is provided.

Item Type: Book Section
Uncontrolled Keywords: Beta-coalescent, Kingman’s paintbox construction, Continuous-state branching processes, Largest block size, Block-counting process
Depositing User: Symplectic Admin
Date Deposited: 20 May 2020 10:22
Last Modified: 18 Jan 2023 23:56
DOI: 10.1007/978-3-319-77643-9_8
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3081329