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arXiv · 1709.08500

The genealogy of Galton-Watson trees

Samuel G. G. Johnston
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Abstract

Take a continuous-time Galton-Watson tree and pick $k$ distinct particles uniformly from those alive at a time $T$. What does their genealogical tree look like? The case $k=2$ has been studied by several authors, and the near-critical asymptotics for general $k$ appear in Harris, Johnston and Roberts (2018). Here we give the full picture.

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Samuel G. G. Johnston. 2017-09-25. The genealogy of Galton-Watson trees. https://doi.org/10.1214/19-ejp355

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