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 Electronic Journal of Probability > Vol. 5 (2000) > Paper 17 open journal systems 


Poisson point process limits in size-biased Galton-Watson trees

Jochen Geiger, Universität Frankfurt


Abstract
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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Pages: 1-12

Published on: July 10, 2000
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Electronic Journal of Probability. ISSN: 1083-6489