Effective conductivity of homogeneous random sets
Some rigorous results in percolation theory are proved. For translation- invariant random subsets of \(R^ d\), constructed using an ergodic dynamical system, the effective conductivity in the infinite volume is defined. Its existence is proved. In some special cases of Bernoulli percolation models, the singularity of the effective conductivity is shown and related to the critical parameter value at which percolation occurs. Some estimates of the conductivity at the critical value are found.
scientific article; zbMATH DE number 4128209