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

  • Arno Siri-JégousseEmail author
  • Linglong Yuan
Conference paper
Part of the Progress in Probability book series (PRPR, volume 73)


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.


Beta-coalescent Kingman’s paintbox construction Continuous-state branching processes Largest block size Block-counting process 

2010 Mathematics Subject Classification

60J25 60F05 92D15 



The authors would like to thank Fabian Freund for some very valuable comments. Arno Siri-Jégousse would like to welcome Raphaël Clodic Griffon, born the day the final version was sent. ASJ is supported by CONACyT Grant CB-2014/243068.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IIMASUniversidad Nacional Autónoma de MéxicoMexico CityMexico
  2. 2.Department of Mathematical SciencesXi’an Jiaotong-Liverpool UniversitySuzhouPeople’s Republic of China

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