Abstract. Functional series with a point-wise random input (the density field of a random set of points x_j ) are considered. The series are rearranged so as the so-called factorial fields of the set x_j appear; the obtained series are called factorial. The basic result of the paper states that the factorial series possess virial property. This means that if a random field u(x) is expanded as a factorial series, the truncation u (x) of the latter after the p-tuple term coincides, in statistical sense, with u(x) to the order n ^p, where n is the number density of the set x_j , p = 1,2, ... . The performance of the factorial series in random media problems is illustrated on the example of steady-state diffusion in a random dispersion of spheres whose sink strength differs from that of the matrix. The full statistical solution of this problem, correct to the order c ^p, is obtained; in particular, the effective sink-strength of the dispersion is found to the same order c ^p with c being the volume fraction of the spheres.

Keywords: functional (Volterra-Wiener) series, random media, correlation functions, effective properties, lossy composites.
AMS (MOS) subject classification: 60H25, 82A42.