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Behavior of the supercritical phase of a continuum percolation model on ℝd

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Hideki Tanemura
Hideki Tanemura*
Affiliation:
Chiba University
*
∗ Postal address: Department of Mathematics, Faculty of Science, Chiba University, Chiba 263, Japan.
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Abstract

A continuum percolation model on is considered. Using a renormalization technique developed by Grimmett and Marstrand, we show a 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.

Keywords

CRITICAL VALUEEFFECTIVE CONDUCTIVITYPOISSON BLOB MODELPOISSON DISTRIBUTIONRENORMALIZATION TECHNIQUE

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 382 - 396
Copyright
Copyright © Applied Probability Trust 1993 

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