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Random fields related to the symmetry classes of second-order symmetric tensors
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0139-0747
University of Illinois at Urbana-Champaign, Urbana, United States.
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 173-185Chapter in book (Refereed)
Abstract [en]

Under the change of basis in the three-dimensional space by means of an orthogonal matrix g, a matrix A of a linear operator is transformed as A → gAg-1 Mathematically, the stationary subgroup of a symmetric matrix under the above action can be either (Formula Presented), when all three eigenvalues of A are different, or (Formula Presented), when two of them are equal, or O(3), when all three eigenvalues are equal. Physically, one typical application relates to dependent quantities like a second-order symmetric stress (or strain) tensor. Another physical setting is that of dependent fields, such as conductivity with such three cases is the conductivity (or, similarly, permittivity, or anti-plane elasticity) second-rank tensor, which can be either orthotropic, transversely isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed point set of the class that is invariant with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 271, p. 173-185
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
Keywords [en]
Random field, Spectral expansion, Symmetry class, Eigenvalues and eigenfunctions, Expansion, Heat conduction, Mathematical operators, Permittivity, Random processes, Stochastic models, Stochastic systems, Tensors, Electric permittivities, Natural representation, Random fields, Spectral expansions, Three dimensional space, Transversely isotropic, Typical application, Matrix algebra
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-41836DOI: 10.1007/978-3-030-02825-1_10Scopus ID: 2-s2.0-85058569471ISBN: 9783030028244 OAI: oai:DiVA.org:mdh-41836DiVA, id: diva2:1274026
Conference
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

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Publisher's full textScopushttps://www.springer.com/gp/book/9783030028244

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Malyarenko, Anatoliy

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