Simple exact treatment of conductance in a random Bethe lattice

Abstract

An exact probabilistic treatment of conduction properties of random Bethe resistor lattices is presented. In the special case of substitutional disorder where a faction 1-p of resistors is removed, the known exact results for the conductance and voltage correlations in the critical region p to p_c are readily given. The simplicity of the method allows a generalization to the case where the remaining fraction p of resistors also has an arbitrary distribution. The case where each element of the lattice is composed of several independently distributed resistive and reactive parts is also discussed.