Journal of Applied Probability

Total internal and external lengths of the Bolthausen-Sznitman coalescent

Götz Kersting, Juan Carlos Pardo, and Arno Siri-Jégousse

Abstract

In this paper we study a weak law of large numbers for the total internal length of the Bolthausen-Sznitman coalescent, thereby obtaining the weak limit law of the centered and rescaled total external length; this extends results obtained in Dhersin and Möhle (2013). An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.

Article information

Source
J. Appl. Probab. Volume 51A (2014), 73-86.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
http://projecteuclid.org/euclid.jap/1417528468

Digital Object Identifier
doi:10.1239/jap/1417528468

Mathematical Reviews number (MathSciNet)
MR3317351

Zentralblatt MATH identifier
1317.60112

Subjects
Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J25: Continuous-time Markov processes on general state spaces 60F05: Central limit and other weak theorems 92D25: Population dynamics (general)

Keywords
Coalescent process Bolthausen-Sznitman coalescent external branch block counting process recursive construction Iksanov-Möhle coupling

Citation

Kersting, Götz; Pardo, Juan Carlos; Siri-Jégousse, Arno. Total internal and external lengths of the Bolthausen-Sznitman coalescent. J. Appl. Probab. 51A (2014), 73--86. doi:10.1239/jap/1417528468. http://projecteuclid.org/euclid.jap/1417528468.


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References

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