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"Behavior of the supercritical phase of a coutinuum percolation model on R^d",

J. Appl. Probab. 30 (1993), no.2, pp.382-396.

A continuum percolation model on R^d (d>=2) is considered. Using a renormalization technique developed by Grimmett and Marstrand, we show continuum analogue of their results. We prove the critical value of the percolation equals the limit of the critical value of a slice as the thickness of the slice tends to infinity. We also prove that the effective conductivity in the model is bounded from below by a positive constant in the supercritical case.
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