Abstract. This work concerns steady state diffusion in a medium containing a random distribution of sinks. The physical properties of the medium are described in terms of geometrical correlation functions, for example, two or three point correlations. Variational principles of classical type are developed and configuration dependent trial fields are substituted into them. Restrictions on certain integrals of the two and three point correlation functions then follow from the avoidance of mathematical contradictions. The consequences of the restrictions and the relationship between the classical variational principles and variational principles of Hashin-Shtrikman type are discussed.