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2000 Poisson point process limits in size-biased Galton-Watson trees
Jochen Geiger
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Electron. J. Probab. 5: 1-12 (2000). DOI: 10.1214/EJP.v5-73


Consider a critical binary continuous-time Galton-Watson tree size-biased according to the number of particles at time $t$. Decompose the population at $t$ according to the particles' degree of relationship with a distinguished particle picked purely at random from those alive at $t$. Keeping track of the times when the different families grow out of the distinguished line of descent and the related family sizes at $t$, we represent this relationship structure as a point process in a time-size plane. We study limits of these point processes in the single- and some multitype case.


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Jochen Geiger. "Poisson point process limits in size-biased Galton-Watson trees." Electron. J. Probab. 5 1 - 12, 2000.


Accepted: 10 July 2000; Published: 2000
First available in Project Euclid: 7 March 2016

zbMATH: 0963.60084
MathSciNet: MR1800073
Digital Object Identifier: 10.1214/EJP.v5-73

Primary: 60J80
Secondary: 60G55

Keywords: Galton-Watson process , limit laws , point process , Random tree

Vol.5 • 2000
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