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A population model for $\Lambda$-coalescents with neutral mutations

Dimulai oleh reborn, Februari 17, 2007, 04:04:52 AM

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A population model for $\Lambda$-coalescents with neutral mutations
Authors: Andreas Nordvall Lagerås
15 pages, 4 figures.
Subj-class: Probability
Journal-ref: Electronic Communications in Probability 12(2007), 9-20

Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $\Lambda$-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by M{\"o}hle (2007).