BooksecrCollected Volumepp. 223–246

Probabilistic aspects of Λ-coalescents in equilibrium and in evolution

  • Götz Kersting

    Goethe-Universität Frankfurt am Main, Germany
  • Anton Wakolbinger

    J. W. Goethe-Universität, Frankfurt a.M., Germany
Probabilistic aspects of Λ-coalescents in equilibrium and in evolution cover
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Abstract

We present approximation methods that lead to law of large numbers and fluctuation results for functionals of Λ-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 of functionals on appropriate time scales. Finally, we review results of Gufler on the representation of evolving Λ-coalescents in terms of the lookdown space.