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

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.