Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/43772
Title: Circulant tensors with applications to spectral hypergraph theory and stochastic process
Authors: Chen, Z
Qi, L 
Keywords: Circulant hypergraphs
Circulant tensors
Directed circulant hypergraphs
Eigenvalues of tensors
Positive semi-definiteness
Issue Date: 2016
Publisher: American Institute of Mathematical Sciences
Source: Journal of industrial and management optimization, 2016, v. 12, no. 4, p. 1227-1247 How to cite?
Journal: Journal of industrial and management optimization 
Abstract: Circulant tensors naturally arise from stochastic process and spectral hypergraph theory. The joint moments of stochastic processes are symmetric circulant tensors. The adjacency, Laplacian and signless Laplacian tensors of circulant hypergraphs are also symmetric circulant tensors. The adjacency, Laplacian and signless Laplacian tensors of directed circulant hypergraphs are circulant tensors, but they are not symmetric in general. In this paper, we study spectral properties of circulant tensors and their applications in spectral hypergraph theory and stochastic process. We show that in certain cases, the largest H-eigenvalue of a circulant tensor can be explicitly identified. In particular, the largest H-eigenvalue of a nonnegative circulant tensor can be explicitly identified. This confirms the results in circulant hypergraphs and directed circulant hypergraphs. We prove that an even order circulant B0 tensor is always positive semi-definite. This shows that the Laplacian tensor and the signless Laplacian tensor of a directed circulant even-uniform hypergraph are positive semi-definite. If a stochastic process is mth order stationary, where m is even, then its mth order moment, which is a circulant tensor, must be positive semi-definite. In this paper, we give various conditions for an even order circulant tensor to be positive semi-definite.
URI: http://hdl.handle.net/10397/43772
ISSN: 1547-5816
EISSN: 1553-166X
DOI: 10.3934/jimo.2016.12.1227
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