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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.

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