On conductivity of composite material composed from thin random layers

We study conductive properties of a composite material, consisting of alternating layers with finite and infinite specific conductivity. On the basis of assumptions that separation boundaries of layers are stochastic functions and the layers thickness $\varepsilon$ (in an oder of magnitude) is infinitely descending we have derived the formula for effective electrical conductivity of the relevant sample for the total current flowing in the direction being normal to a layer surface.