Journal of Statistical Physics

, Volume 64, Issue 3–4, pp 843–850 | Cite as

Euler characteristic and related measures for random geometric sets

  • K. R. Mecke
  • H. Wagner
Short Communications


By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.

Key words

Random sets integral geometry Minkowski functionals Euler characteristic continuum percolation 


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • K. R. Mecke
    • 1
  • H. Wagner
    • 1
  1. 1.Sektion Physik der Universität MünchenMünchen 2Germany

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