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Isotropic random tangential vector fields on spheres

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  • Lu, Tianshi

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.

Suggested Citation

  • Lu, Tianshi, 2024. "Isotropic random tangential vector fields on spheres," Statistics & Probability Letters, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:stapro:v:213:y:2024:i:c:s016771522400141x
    DOI: 10.1016/j.spl.2024.110172
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    References listed on IDEAS

    as
    1. Minjie Fan & Debashis Paul & Thomas C. M. Lee & Tomoko Matsuo, 2018. "Modeling Tangential Vector Fields on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1625-1636, October.
    2. Chunsheng Ma & Anatoliy Malyarenko, 2020. "Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 33(1), pages 319-339, March.
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