Vol. 2, No. 2, 2014

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ISSN: 2325-3444 (e-only)
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Statistically isotropic tensor random fields: Correlation structures

Anatoliy Malyarenko and Martin Ostoja-Starzewski

Vol. 2 (2014), No. 2, 209–231

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 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 = 3, and those by Lomakin, when V is the space of symmetric second-rank tensors over 3. Our solution involves an analogue of the classical Clebsch–Gordan coefficients.

isotropic tensor random field, group representation, Godunov–Gordienko coefficients
Mathematical Subject Classification 2010
Primary: 60G60
Secondary: 74A40
Received: 12 February 2013
Revised: 15 July 2013
Accepted: 11 September 2013
Published: 9 June 2014

Communicated by Eric A. Carlen
Anatoliy Malyarenko
Division of Applied Mathematics
Mälardalen University
Box 883
Högskoleplan 1
SE-721 23 Västerås
Martin Ostoja-Starzewski
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
1206 W. Green Street
Urbana, IL 61801-2906
United States