Isotropic random tangential vector fields on spheres
Lu, Tianshi
Lu, Tianshi
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2024
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Article
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Helmholtz-Hodge decomposition,Isotropic random vector field,Karhunen-Loève expansion
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Lu, T. Isotropic random tangential vector fields on spheres. (2024). Statistics and Probability Letters, 213, art. no. 110172. DOI: 10.1016/j.spl.2024.110172
Abstract
In this paper we characterized isotropic random tangential vector fields on d-spheres for d?1 by the cross-covariance, and derived their Karhunen-Loève expansion. The tangential vector field can be decomposed into a curl-free part and a divergence-free part by the Helmholtz-Hodge decomposition. We proved that the two parts can be correlated on a 2-sphere, while they must be uncorrelated on a d-sphere for d?3. On a 3-sphere, the divergence-free part can be further decomposed into two isotropic flows. © 2024 Elsevier B.V.
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Elsevier B.V.
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Statistics and Probability Letters
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0167-7152