Isotropic random tangential vector fields on spheres

Tianshi Lu

Statistics & Probability Letters, 2024, vol. 213, issue C

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.

Keywords: Isotropic random vector field; Karhunen–Loève expansion; Helmholtz–Hodge decomposition (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110172

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