Advertisement

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

  • J. Geiger
  • G. Kersting
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Aldous]
    D.J. Aldous, The continuum random tree II: an overview, Proc. Durham Symp. Stoch. Analysis 1990, p. 23–70, Cambridge University Press, 1991.Google Scholar
  2. [Geigerl]
    J. Geiger, Contour processes of random trees, Stochastic Partial Differential Equations, p. 72–96, London Mathematical Society Lecture Notes, vol. 216, Cambridge University Press, 1995.Google Scholar
  3. [Geiger2]
    J. Geiger, Zufällige Bäume und Punktprozesse, PhD thesis. Frankfurt/Main, 1994.Google Scholar
  4. [LeGall]
    J.F. Legall, Marches aleatoires, mouvement brownien et processus de branchement, Seminaire de Probabilites XXIII, p. 258–274 Lecture Notes in Math. 1372, Springer, 1989.Google Scholar
  5. [Lyons]
    R. LYONS, Probability and Trees, Lecture Notes (unpublished), Indiana, 1994.Google Scholar
  6. [Neveu, Pitman]
    Pitman] J. Neveu and J.W. ITMANN, The branching process in a Brown-ian excursion, Seminaire de Probabilites XXIII, p. 248–257, Lecture Notes in Math. 1372, Springer, 1989.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • J. Geiger
    • 1
  • G. Kersting
    • 1
  1. 1.Fachbereich MathematikUniversität FrankfurtFrankfurt/MainGermany

Personalised recommendations