Percolation in a multiscale Boolean model

Details Percolation in a multiscale Boolean model Percolation in a multiscale Boolean model

2010-09-20

arxiv.org/abs/1009.3719v3

Mathematics

Probability

Scientific paper

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 $n^{\textrm{th}}$ 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.

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