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Genealogies of regular exchangeable coalescents with applications to sampling

Vlada Limic (2012)

Annales de l'I.H.P. Probabilités et statistiques

This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as 𝛯 -coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number of active lineages were obtained by the author in a previous work. Analogous results for the number of active mutation-free lineages and the combined lineage lengths are derived using the same martingale-based technique. They are given in terms of convergence in...

Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property

Cyril Labbé (2014)

Annales de l'I.H.P. Probabilités et statistiques

We encode the genealogy of a continuous-state branching process associated with a branching mechanism 𝛹 – or 𝛹 -CSBP in short – using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property – the existence of an ancestor from which the entire population descends asymptotically – and give a necessary and sufficient condition on the 𝛹 -CSBP for...

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