2009/08/17 by Peter Pfaffelhuber, Pfaffelhuber, Peter, Anton Wakolbinger +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60K35 #Evolution and Genetic Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.0908.2444
openalex publication_date 2009/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.