Statistically isotropic tensor random fields: Correlation structures

Anatoliy Malyarenko, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


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 R3. 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 = R3, and those by Lomakin, when V is the space of symmetric second-rank tensors over R3. Our solution involves an analogue of the classical Clebsch-Gordan coefficients.

Original languageEnglish (US)
Pages (from-to)209-231
Number of pages23
JournalMathematics and Mechanics of Complex Systems
Issue number2
StatePublished - 2014


  • Godunov-Gordienko coefficients
  • Group representation
  • Isotropic tensor random field

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Numerical Analysis
  • Computational Mathematics

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