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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

Abstract

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.

Citation

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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. https://doi.org/10.1214/17-ECP93

Information

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

Subjects:
Primary: 60J70
Secondary: 60F05, 92D25

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