The tree length of an evolving coalescent

Details The tree length of an evolving coalescent The tree length of an evolving coalescent

2009-08-17

arxiv.org/abs/0908.2444v3

Mathematics

Probability

23 pages, 6 figures

Scientific paper

A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the population size tends to infinity, to a limit process with cadlag paths, infinite infinitesimal variance, and a Gumbel distribution as its equilibrium.

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