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On the number of collisions in lambda-coalescents. (English) Zbl 1190.60061

Summary: 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 \(0 < \alpha < 1\).

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K15 Markov renewal processes, semi-Markov processes