Exact conditions on physically realizable correlation functions of random media

Algorithms have been developed recently to construct realizations of random media with specified statistical correlation functions. There is a need fo r the formulation of exact conditions on the correlation functions in order to ensure that hypothetical correlation functions are physically realizabl e. Here we obtain positivity conditions on certain integrals of the autocor relation function of d-dimensional statistically homogeneous media and of s tatistically isotropic media. These integral conditions are then applied to test various classes of autocorrelation functions. Finally, we note some i ntegral conditions on the three-point correlation function. (C) 1999 Americ an Institute of Physics. [S0021- 9606(99)51343-3].