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2017 Second order behavior of the block counting process of beta coalescents
Yier Lin, Bastien Mallein
Electron. Commun. Probab. 22: 1-8 (2017). DOI: 10.1214/17-ECP93


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 [2] proved a law of large numbers for this quantity. Recently, Limic and Talarczyk [9] 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.


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Yier Lin. Bastien Mallein. "Second order behavior of the block counting process of beta coalescents." Electron. Commun. Probab. 22 1 - 8, 2017.


Received: 21 February 2017; Accepted: 11 October 2017; Published: 2017
First available in Project Euclid: 15 November 2017

zbMATH: 1378.60109
MathSciNet: MR3724559
Digital Object Identifier: 10.1214/17-ECP93

Primary: 60J70
Secondary: 60F05 , 92D25

Keywords: beta coalescent , central limit theorem , Continuous-state branching process , Lamperti transform


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