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September 2014 Minimal clade size in the Bolthausen-Sznitman coalescent
Fabian Freund, Arno Siri-Jégousse
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J. Appl. Probab. 51(3): 657-668 (September 2014). DOI: 10.1239/jap/1409932665

Abstract

In this article we show the asymptotics of distribution and moments of the size Xn of the minimal clade of a randomly chosen individual in a Bolthausen-Sznitman n-coalescent for n → ∞. The Bolthausen-Sznitman n-coalescent is a Markov process taking states in the set of partitions of {1, . . ., n}, where 1, . . ., n are referred to as individuals. The minimal clade of an individual is the equivalence class the individual is in at the time of the first coalescence event this individual participates in. We also provide exact formulae for the distribution of Xn. The main tool used is the connection of the Bolthausen-Sznitman n-coalescent with random recursive trees introduced by Goldschmidt and Martin (2005). With it, we show that Xn - 1 is distributed as the size of a uniformly chosen table in a standard Chinese restaurant process with n - 1 customers.

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Fabian Freund. Arno Siri-Jégousse. "Minimal clade size in the Bolthausen-Sznitman coalescent." J. Appl. Probab. 51 (3) 657 - 668, September 2014. https://doi.org/10.1239/jap/1409932665

Information

Published: September 2014
First available in Project Euclid: 5 September 2014

zbMATH: 1320.60132
MathSciNet: MR3256218
Digital Object Identifier: 10.1239/jap/1409932665

Subjects:
Primary: 60C05
Secondary: 05C80, 60F05, 60G09, 60J27, 92D25

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 3 • September 2014
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