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The Beta coalescents are stochastic processes modeling the genealogy of apopulation. They appear as the rescaled limits of the genealogical trees ofnumerous stochastic population models. In this article, we take interest in thenumber of blocs at small times in the Beta coalescent. Berestycki, Berestyckiand Schweinsberg proved a law of large numbers for this quantity. Recently,Limic and Talarczyk proved that a functional central limit theorem holds aswell. We give here a simple proof for an unidimensional version of this result,using a coupling between Beta coalescents and continuous-time branchingprocesses.

Second order behavior of the block counting process of beta coalescents