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The coincidence of critical points in Poisson percolation models. (English. Russian original) Zbl 0661.60122
Theory Probab. Appl. 32, No. 3, 547-550 (1987); translation from Teor. Veroyatn. Primen. 32, No. 3, 603-606 (1987).
The authors consider a continuous percolation model in $${\mathbb{R}}^ d:$$ percolation through clusters of “defects” of variable random shape of which the centers have Poisson distribution with intensity $$\lambda$$. We can define two percolation tresholds $$\lambda_ T$$ and $$\lambda_ H$$. The first one is the point of divergence of mean cluster size and the second is the maximal value of $$\lambda$$ for which the probability of existence of an unbounded cluster is equal to zero. For a wide class of situations the coincidence between $$\lambda_ T$$ and $$\lambda_ H$$ is proved (for example in the case of a finite number of shapes of defects).
Reviewer: P.A.Kučment

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation
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