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Size-biased and conditioned random splitting trees. (English) Zbl 0889.60089
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:
60J80Branching processes
60G55Point processes
60K25Queueing theory