The genealogy of Galton-Watson trees

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.

35 pages, 2 figures

References in corpus (1)

• On the genealogy and coalescence times of Bienaymé-Galton-Watson branching processes

Cited by in corpus (2)

• Some properties of stationary continuous state branching processes
• Coalescence in small generations for the diffusive randomly biased walk on Galton-Watson trees