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Nonuniversality and continuity of the critical covered volume fraction in continuum percolation. (English) Zbl 0828.60083
Summary: 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.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
Full Text: DOI
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