Remarks on percolation and transport in networks with a wide range of bond strengths

Abstract

In conventional percolation problems, there is no simple relation between the transport exponents and the critical exponents which describe geometric properties of the percolating clusters. In several problems involving bonds with a wide range of conductance, however, it has been found that there does exist a simple relation between the transport exponent and the geometric exponent describing the divergence of the correlation length. We give a brief review of these problems.