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October 2015 The fixation line in the ${\Lambda}$-coalescent
Olivier Hénard
Ann. Appl. Probab. 25(5): 3007-3032 (October 2015). DOI: 10.1214/14-AAP1077

Abstract

We define a Markov process in a forward population model with backward genealogy given by the $\Lambda$-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two applications are discussed. The probability that the $n$-coalescent is deeper than the $(n-1)$-coalescent is studied. The distribution of the number of blocks in the last coalescence of the $n$-$\operatorname{Beta}(2-\alpha,\alpha)$-coalescent is proved to converge as $n\rightarrow\infty$, and the generating function of the limiting random variable is computed.

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Olivier Hénard. "The fixation line in the ${\Lambda}$-coalescent." Ann. Appl. Probab. 25 (5) 3007 - 3032, October 2015. https://doi.org/10.1214/14-AAP1077

Information

Received: 1 August 2013; Revised: 1 September 2014; Published: October 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1325.60124
MathSciNet: MR3375893
Digital Object Identifier: 10.1214/14-AAP1077

Subjects:
Primary: 60G55, 60J25, 60J80

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 2015
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