# Probabilistic aspects of $\Lambda$-coalescents in equilibrium and in evolution

@article{Kersting2020ProbabilisticAO, title={Probabilistic aspects of \$\Lambda\$-coalescents in equilibrium and in evolution}, author={G{\"o}tz Kersting and A. Wakolbinger}, journal={arXiv: Probability}, year={2020} }

We present approximation methods which lead to law of large numbers and fluctuation results for functionals of $\Lambda$-coalescents, both in the dust-free case and in the case with a dust component. Our focus is on the tree length (or total branch length) and the total external branch length, as well as the time to the most recent common ancestor and the size of the last merger. In the second part we discuss evolving coalescents. For certain Beta-coalescents we analyse fluctuations of a class…

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