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Zbl 0889.60089
Geiger, J.
Size-biased and conditioned random splitting trees. (English)
[J] Stochastic Processes Appl. 65, No.2, 187-207 (1996). ISSN 0304-4149

Summary: Random splitting trees share the striking independence properties of the continuous time binary Galton-Watson tree. They can be represented by Poisson point processes, and their contour processes are strong Markov processes. Here we study splitting trees conditioned on extinction, respectively non-extinction as well as size-biased splitting trees. We give explicit probabilistic constructions of those trees by decomposing them into independent parts along a distinguished line of descent. The size-biased trees are shown to have stationary contour processes. Splitting trees are related to M/G/1-queueing systems which allows to translate the results on the trees into statements on the queues.

MSC 2000:: *60J80 Branching processes
60G55 Point processes
60K25 Queueing theory

Keywords: random tree; Galton-Watson process; depth-first search; Poisson point process; size-biasing method; M/G/1-queue

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