1 results
Behavior of the supercritical phase of a continuum percolation model on ℝd
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 30 / Issue 2 / June 1993
- Published online by Cambridge University Press:
- 14 July 2016, pp. 382-396
- Print publication:
- June 1993
-
- Article
- Export citation
-
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.
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.