Abstract

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.

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Mathematical Subject Classification 2010

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