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Statistics at the tip of a branching random walk, and simple models of evolution with selection.

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The statistics at the tip of a branching random walk can be studied using the Fisher-KPP equation. The whole limiting measure, at the tip, can be understood in terms of the way the delay of a traveling wave solution of the F-KPP equation depends on its initial condition. Several analytical properties of the distribution of the distances between the rightmost particles can be predicted. This work was motivated by the study of the statistical properties of genealogies of evolving populations under selection.

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