Genealogies in Expanding Populations
Rick Durrett and Wai-Tong (Louis) Fan
Abstract.
Mueller and Tribe have shown that rescaled long-range voter models in one-dimension converge to a Wright-Fisher SPDE,
also known as a stochastic Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) wave.
Recently Hallatschek and Nelson have described the asymptotic behavior of genealogies in a closely related model.
Their answer is expressed in terms of a diffusion in a very singular random environment. Here we prove rigorous results
that partially confirm their analysis. Brunet et al. have conjectured that genealogies of all models in the FKPP
universality class are described by the Bolthausen-Sznitman coalescent. However, in the model we study there are
no simultaneous coalescences.
Preprint
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