On the number of collisions in $\Lambda$-coalescents

Abstract

We examine the total number of collisions $C_n$ in the $\Lambda$-coalescent process which starts with $n$ particles. A linear growth and a stable limit law for $C_n$ are shown under the assumption of a power-like behaviour of the measure $\Lambda$ near 0 with exponent $0<\alpha <1$.

18 pages