# The fixation line in the ${\Lambda}$-coalescent

@article{Henard2015TheFL,
title={The fixation line in the \$\{\Lambda\}\$-coalescent},
author={Olivier H'enard},
journal={Annals of Applied Probability},
year={2015},
volume={25},
pages={3007-3032}
}
• Olivier H'enard
• Published 2 July 2013
• Mathematics
• Annals of Applied Probability
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…

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