Journal of Statistical Physics

, Volume 75, Issue 1–2, pp 123–134 | Cite as

Nonuniversality and continuity of the critical covered volume fraction in continuum percolation

  • Ronald Meester
  • Rahul Roy
  • Anish Sarkar


We establish, using mathematically rigorous methods, that the critical covered volume fraction (CVF) for a continuum percolation model with overlapping balls of random sizes is not a universal constant independent of the distribution of the size of the balls. In addition, we show that the critical CVF is a continuous function of the distribution of the radius random variable, in the sense that if a sequence of random variables converges weakly to some random variable, then the critical CVF based on these random variables converges to the critical CVF of the limiting random variable.

Key Words

Poisson point process continuum percolation critical intensity covered volume fraction 


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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Ronald Meester
    • 1
  • Rahul Roy
    • 2
  • Anish Sarkar
    • 2
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtThe Netherlands
  2. 2.Indian Statistical InstituteNew DelhiIndia

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