The genealogy of Galton-Watson trees. (English) Zbl 1467.60065
Summary: 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 [S. C. Harris et al., Ann. Appl. Probab. 30, No. 3, 1368–1414 (2020; Zbl 1472.60141)]. Here we give the full picture.
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 60J85 | Applications of branching processes |
Citations:
Zbl 1472.60141References:
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