Abstract. The problem of heat conduction through a random dispersion of nonoverlapping spheres is considered. The full stochastic description of the random temperature field, q(x), in the dispersion is obtained in the form of a factorial functional series. Such series, recently introduced in [1], have the important property that their truncations after the p-tuple term give results for all needed multipoint correlation functions which are correct to the order c; here c is the volume fraction of the spheres, p=1,2,... . The procedure of identification of the kernels in the series is considered in detail for the case p=2 so that the full stochastic description of q(x) correct to the order c, is obtained in a closed form. In particular, the effective conductivity of the dispersion is found to the same order and shown to coincide with the known formula of D. Jeffrey [2].

1. K. Z. Markov. On the factorial functional series and their application to random media. SIAM J. Appl. Math., 51, 1991, No 1, 172-186.
2. D. J. Jeffrey. Conduction through a random suspension of spheres. Proc. Roy. Soc. London, A335, 1973, 355-367.