Poisson point process limits in size-biased Galton-Watson trees
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
Publication Date: July 10, 2000
DOI: 10.1214/EJP.v5-73
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