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Excheangable partitions derived from Markovian coalescents. (English) Zbl 1147.60022
This paper investigates the problems of random coalescent process. The idea comes from biological studies for genealogy of haploid model: given a large population with many generations. As you track further, the family lines coalesce with each other, eventually all terminating at a common ancestor of current generation. The authors show that the basic integral representation of transition rates for the so-called $$\Lambda$$-coalescent is forced by sampling consistency under more general assumptions on the coalescent process. Exploiting an analogy with the theory of regenerative partition structures, they provide various characterizations of associated partition structures in terms of discrete-time Markov chains.

MSC:
 60G09 Exchangeability for stochastic processes 60C05 Combinatorial probability
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References:
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