Statistical Properties of Genealogical Trees
B. Derrida
2005, v.11, Issue 2
ABSTRACT
One can associate to the genealogical tree of each individual the distribution of repetitions of his ancestors, at a number $g$ of generations in the past. By solving a simple model of a population of constant size $N$ with random mating, one can show that this distribution of repetitions reaches a stationary shape, with a non trivial power law which can be calculated analytically. By comparing the genealogical trees of two distinct individuals, one can also show that the two trees become identical within a number $\log N$ of generations.
Keywords: genealogical tree,distribution of repetitions of ancestors
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