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Zbl 0867.60061
Geiger, J.; Kersting, G.
Depth-first search of random trees, and Poisson point processes. (English)
[A] Athreya, Krishna B. (ed.) et al., Classical and modern branching processes. Proceedings of the IMA workshop, Minneapolis, MN, USA, June 13--17, 1994. New York, NY: Springer. IMA Vol. Math. Appl. 84, 111-126 (1997). ISBN 0-387-94872-4/hbk

Summary: Random planar trees can be represented by point processes in the upper positive quadrant of the plane. This proves helpful in studying the distance-from-the-root process of the depth-first search: For certain splitting trees this so-called contour process is seen to be Markovian and its jump intensities can be explicitly calculated. The representation via point processes also allows to construct locally infinite splitting trees. Moreover we show how to generate Galton-Watson branching trees with possibly infinite offspring variance out of Poisson point processes.

MSC 2000:: *60J80 Branching processes
60G55 Point processes
60J25 Markov processes with continuous parameter

Keywords: random tree; depth-first search; branching process; contour process; Poisson point process; exchangeable random variables

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