The Beta coalescents are stochastic processes modeling the genealogy of a population. They appear as the rescaled limits of the genealogical trees of numerous stochastic population models. In this article, we take interest in the number of blocs at small times in the Beta coalescent. Berestycki, Berestycki and Schweinsberg  proved a law of large numbers for this quantity. Recently, Limic and Talarczyk  proved that a functional central limit theorem holds as well. We give here a simple proof for an unidimensional version of this result, using a coupling between Beta coalescents and continuous-time branching processes.
"Second order behavior of the block counting process of beta coalescents." Electron. Commun. Probab. 22 1 - 8, 2017. https://doi.org/10.1214/17-ECP93