STATISTICALLY ISOTROPIC TENSOR RANDOM FIELDS: CORRELATION STRUCTURES

Let V be a real finite-dimensional vector space. We introduce some physical problems that may be described by V-valued homogeneous and isotropic random fields on R-3. We propose a general method for calculation of expectations and two-point correlation functions of such fields. Our results are equivalent to classical results by Robertson, when V = R-3, and those by Lomakin, when V is the space of symmetric second-rank tensors over R-3. Our solution involves an analogue of the classical Clebsch-Gordan coefficients.