  General properties of the effective conductivity sigma_e of planar isotropic
randomly inhomogeneous two-phase self-dual systems are investigated. A new
approach for finding out sigma_e of random systems based on a duality, a series
expansion in the inhomogeneous parameter z and additional assumptions, is
proposed. Two new approximate expressions for sigma_e at arbitrary values of
phase concentrations are found. They satisfy all necessary inequalities,
symmetries, including a dual one, and reproduce known results in various
limiting cases. Two corresponding models with different inhomogeneity
structures, whose sigma_e coincide with these expressions, are constructed.
First model describes systems with a finite maximal characteristic scale of the
inhomogeneities. In this model sigma_e is a solution of the approximate
functional equation, generalizing the duality relation. The second model is
constructed from squares with random layered structure. The difference of
sigma_e for these models means a nonuniversality of the effective conductivity
even for binary random self-dual systems. The first explicit expression for
sigma_e can be used also for approximate description of various inhomogeneous
systems with compact inclusions of the second phase. The percolation problem of
these models is briefly discussed.
