On the time to absorption in $Λ$-coalescents

Published 20 Dec 2017 in math.PR | (1712.07553v1)

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.

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