Approximate symmetry laws for percolation in complex systems: Percolation in polydisperse composites.

The concept of so-called global symmetry of percolation models is discussed and extended to multicolored models. An integral equation is obtained, which determines the partial percolation probabilities P(a) for sites of color a. This equation is applied to a polydisperse particulate composite: a mixture of conducting (of relative fraction x(m)) and nonconducting spheres with distributions of sizes n(m)(R) and n(i)(R), respectively.