A general formulation is developed for calculating the mean neutron flux in spatially random media. It is based upon Keller's first order smoothing approximation and starts from the integral form of the transport equation in which the number densities of the various nuclear species are considered as stationary random variables. The mean flux is shown to be described by a linear integral equation. In some special cases this has been solved. In particular, for a purely absorbing medium we calculate the flux in the neighborhood of point, line and plane sources and demonstrate the importance of the degree of anisotropy in the correlation function. We also obtain an analytical expression for the collision probability in a spatially random medium and compare this with its deterministic analog.

An explicit solution for the mean flux in an infinite medium is obtained in terms of a general source distribution using Fourier transforms. Using image pile theory we are able to calculate the effect of randomness on the critical size of a body. We can show that, for a fissile material, spatial randomness always increases the reactivity of the mixture.