@inbook{57ac5094f25645e788d55468a184a1e1,

title = "A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents",

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 Poincar{\'e} 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.",

keywords = "Beta-coalescent, Block-counting process, Continuous-state branching processes, Kingman{\textquoteright}s paintbox construction, Largest block size",

author = "Arno Siri-J{\'e}gousse and Linglong Yuan",

note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.",

year = "2018",

doi = "10.1007/978-3-319-77643-9_8",

language = "English",

series = "Progress in Probability",

publisher = "Birkhauser",

pages = "219--234",

booktitle = "Progress in Probability",

}