On the time to absorption in $Λ$-coalescents

Götz Kersting, Anton Wakolbinger

Published 2017-12-20Version 1

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.