The bilocal approximation for the effective dielectric constant of an isotropic random medium

The bilocal approximation in strong fluctuation theory leads to an expression for the effective dielectric constant of a random medium. A detailed study of this expression is made for the case of a medium characterized by an isotropic correlation function. The effective dielectric constant is shown to obey an equation involving an integral containing the correlation function, the free space propagation constant, the quasistatic dielectric constant, and the effective dielectric constant itself, Numerical methods for solution are suggested. The low frequency behavior is also examined. The leading correction term to the quasistatic dielectric constant is shown to be different than previously deduced expressions.