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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