Electronic Communications in Probability

Second order behavior of the block counting process of beta coalescents

Yier Lin and Bastien Mallein

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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.

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 61, 8 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1510736418

Digital Object Identifier
doi:10.1214/17-ECP93

Mathematical Reviews number (MathSciNet)
MR3724559

Zentralblatt MATH identifier
1378.60109

Subjects
Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 60F05: Central limit and other weak theorems 92D25: Population dynamics (general)

Keywords
Beta coalescent central limit theorem continuous-state branching process Lamperti transform

Rights
Creative Commons Attribution 4.0 International License.

Citation

Lin, Yier; Mallein, Bastien. Second order behavior of the block counting process of beta coalescents. Electron. Commun. Probab. 22 (2017), paper no. 61, 8 pp. doi:10.1214/17-ECP93. https://projecteuclid.org/euclid.ecp/1510736418


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References

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