Abstract
We study the multiscale (fractal) percolation in dimension greater than or equal to 2, where the model at each level is the Poisson Boolean model [[λ, ρ]]. Also, the random radius ρ is supposed to be unbounded. We prove that if the rate λ of Poisson field is less than some critical value, then by choosing the scaling parameter large enough one can assure that there is no multiscale percolation. Another result of this paper is that if the expectation of ρ 2αd is finite, then the expectation of the size of the cluster raised to the power α is also finite for small λ, which is a generalization of one of the results of [8].
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