We developed a stochastic transport theory for the calculation of the
ac-conductivity in two-phase mixture materials (with high interface co
nductance). A perturbation around the different configurational interf
ace paths is introduced by using the Effective Medium Approximation (E
MA), Data of LiI conductivity after the addition of an insulating seco
nd phase Al2O3 show that our approach describes the main features of t
he ac-conductivity. The dielectric constant and the static effective c
apacitance, as a function of the concentration of the insulating mater
ial, are compared against previous Monte Carlo simulations and Renorma
lization Group results. Conductivity (Cole-Cole plots) and dielectric
properties of dispersed ionic conductors are studied in a self-consist
ency way, A random walk in a random-resistor network and the use of an
effective electric circuit are presented in order to describe all the
features of the ac-response in these materials.