Chapter

Classical and Modern Branching Processes

Volume 84 of the series The IMA Volumes in Mathematics and its Applications pp 111-126

Depth—First Search of Random Trees, and Poisson Point Processes

  • J. GeigerAffiliated withFachbereich Mathematik, Universität Frankfurt
  • , G. KerstingAffiliated withFachbereich Mathematik, Universität Frankfurt

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Abstract

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—theroot 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.

Key words

Random tree depth—first search branching process contour process Poisson point process exchangeable random variables