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arXiv · 1709.07633

On a coalescence process and its branching genealogy

Nicolas Grosjean·Thierry Huillet
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Abstract

We define and analyze a coalescent process as a recursive box-filling process whose genealogy is given by an ancestral time-reversed, time-inhomogeneous Bienyam\'{e}-Galton-Watson process. Special interest is on the expected size of a typical box and its probability of being empty. Special cases leading to exact asymptotic computations are investigated when the coalescing mechanisms are either linear-fractional or quadratic.

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Nicolas Grosjean, Thierry Huillet. 2017-09-22. On a coalescence process and its branching genealogy. https://doi.org/10.1017/jpr.2016.71

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