Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 22 (2017), paper no. 61, 8 pp.
Second order behavior of the block counting process of beta coalescents
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.
Electron. Commun. Probab., Volume 22 (2017), paper no. 61, 8 pp.
Received: 21 February 2017
Accepted: 11 October 2017
First available in Project Euclid: 15 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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