The size of the last merger and time reversal in $\Lambda$-coalescents

@article{Kersting2018TheSO,
  title={The size of the last merger and time reversal in \$\Lambda\$-coalescents},
  author={G{\"o}tz Kersting and Jason Schweinsberg and A. Wakolbinger},
  journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  year={2018}
}
Author(s): Kersting, Goetz; Schweinsberg, Jason; Wakolbinger, Anton | Abstract: We consider the number of blocks involved in the last merger of a $\Lambda$-coalescent started with $n$ blocks. We give conditions under which, as $n \to \infty$, the sequence of these random variables a) is tight, b) converges in distribution to a finite random variable or c) converges to infinity in probability. Our conditions are optimal for $\Lambda$-coalescents that have a dust component. For general $\Lambda… 
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