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Exploring the Structure of Anisotropic Random Fields on the Sphere — arXiv:2609.32538

Source

arXiv (en)

Original

https://arxiv.org/abs/2609.32538

License (as archived)

CC0-1.0

Archived

2026-10-07T23:23:41.484Z

SHA-256 of the archived text

215628444d687ae2f99ec43f48c485940b055cd5f617c59a81ecc0af0fd6abd9

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https://metraipolis.com/documento/dc_a6da35ec79b0

How to cite

Exploring the Structure of Anisotropic Random Fields on the Sphere — arXiv:2609.32538 — arXiv (en), https://arxiv.org/abs/2609.32538 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a6da35ec79b0 (Metraipolis archive dc_a6da35ec79b0, sha256 215628444d687ae2f99ec43f48c485940b055cd5f617c59a81ecc0af0fd6abd9)

@misc{dca6da35ec79b0,
  title = {Exploring the Structure of Anisotropic Random Fields on the Sphere — arXiv:2609.32538},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.32538},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a6da35ec79b0; sha256 215628444d687ae2f99ec43f48c485940b055cd5f617c59a81ecc0af0fd6abd9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.32538. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper addresses fundamental questions about the existence and structure of isotropic and anisotropic spherical random fields and the properties of composite transformations of isotropic fields. It introduces a hierarchical structure comprising several classes of anisotropic random fields, using geometric and spectral approaches, and provides a geometric--spectral classification of second-order anisotropy on $\mathbb{S}^2$. We characterize feasible isotropic and anisotropic scenarios and identify those that, in principle, cannot occur, in contrast to the case of random fields in Euclidean space. Furthermore, we establish connections between geometric invariance properties and the structure of the spectral covariance matrix of spherical random fields. The obtained results lay the foundations for applications in statistics and data analysis, providing guidance on feasible models, their spectral representations, and appropriate sampling schemes for parameter estimation or anisotropy hypothesis testing for spherical data.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.32538 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T23:02:49.349Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).