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Percolation in a multiscale Boolean model. (English) Zbl 1296.60262
Summary: We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model.
The scale factor of the $$n$$th copy is $$\rho^{-n}$$. We prove, under optimal integrability assumptions, that no percolation occurs in the multiscale Boolean model for large enough $$\rho$$ if the rate of the Boolean model is below some critical value.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60D05 Geometric probability and stochastic geometry 82B43 Percolation
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