The genealogy of Galton-Watson trees

The genealogy of Galton-Watson trees

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 an...

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Veröffentlicht in:arXiv.org 2019-10
1. Verfasser: Johnston, Samuel G G
Format: Artikel
Sprache:eng
Schlagworte:
Genealogy
Markov analysis
Mathematics - Probability
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Beschreibung
Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1709.08500