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

TL;DR

This paper establishes a law of large numbers and a central limit theorem for the absorption time of Lambda-coalescents starting from n blocks, using approximation techniques involving drifted subordinators.

Contribution

It introduces new probabilistic limit theorems for the absorption time in Lambda-coalescents, expanding understanding of their asymptotic behavior.

Findings

Law of large numbers for absorption time

Central limit theorem for absorption time

Approximation of block-counting process using drifted subordinator

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.