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[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.]
Published: Jun 27, 2018
Keywords: Beta-coalescent; Kingman’s paintbox construction; Continuous-state branching processes; Largest block size; Block-counting process; 60J25; 60F05; 92D15
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