Florian Gaiser, Martin Möhle
Published 2016-03-30Version 1
We study the block counting process and the fixation line of exchangeable coalescents. Formulas for the infinitesimal rates of both processes are provided. It is shown that the block counting process is Siegmund dual to the fixation line. For exchangeable coalescents restricted to a sample of size n and with dust we provide a convergence result for the block counting process as n tends to infinity. The associated limiting process is related to the frequencies of singletons of the coalescent. Via duality we obtain an analog convergence result for the fixation line of exchangeable coalescents with dust. The Dirichlet coalescent and the Poisson-Dirichlet coalescent are studied in detail.
On the block counting process and the fixation line of the Bolthausen-Sznitman coalescent
The Mittag-Leffler process and a scaling limit for the block counting process of the Bolthausen-Sznitman coalescent
Scaling limits for the block counting process and the fixation line of a class of $Λ$-coalescents
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