On the time to absorption in $\Lambda$-coalescents

Götz Kersting; Anton Wakolbinger

On the time to absorption in $\Lambda$-coalescents

Probability 2017-12-21 v1

Authors: Götz Kersting , Anton Wakolbinger

Abstract

We present a law of large numbers and a central limit theorem for the time to absorption of $\Lambda$ -coalescents, started from $n$ blocks, as $n \to \infty$ . The proofs rely on an approximation of the logarithm of the block-counting process of $\Lambda$ -coalescents with a dust component by means of a drifted subordinator.

Cite

@article{arxiv.1712.07553,
  title  = {On the time to absorption in $\Lambda$-coalescents},
  author = {Götz Kersting and Anton Wakolbinger},
  journal= {arXiv preprint arXiv:1712.07553},
  year   = {2017}
}

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15 pages

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