On asymptotics of the beta-coalescents

Details On asymptotics of the beta-coalescents On asymptotics of the beta-coalescents

2012-03-14

arxiv.org/abs/1203.3110v1

Mathematics

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We show that the total number of collisions in the exchangeable coalescent process driven by the beta $(1,b)$ measure converges in distribution to a 1-stable law, as the initial number of particles goes to infinity. The stable limit law is also shown for the total branch length of the coalescent tree. These results were known previously for the instance $b=1$, which corresponds to the Bolthausen-Sznitman coalescent. The approach we take is based on estimating the quality of a renewal approximation to the coalescent in terms of a suitable Wasserstein distance. Application of the method to the beta $(a,b)$-coalescents with $0

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