Derivation of an equation to calculate the average conductivity of random networks

This paper deals with the derivation of a formula developed empirically in a previous article. The equation allows the calculation of the average electrical conductivity of two-component random media over the whole range of fraction and a wide range of resistivity ratio of the components. Motivated by the good agreement with numerical and experimental data a physically based derivation of the equation is performed considering the Bose–Einstein statistics. There exist now a physical picture which enables a deeper insight in the characteristics of electrically conducting random networks.