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We establish optimal estimates for its angular power spectrum $\\{d_\\ell, \\ell = 0, 1, 2, \\ldots\\}$, and then exploit its high-frequency behavior to establish the property of its strong local nondeterminism of $B$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.05021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.ST","submitted_at":"2017-07-17T07:13:49Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2312c33901fc26c6f9e379bec66ad5b0991a656d3932a9ed248f8c0801e029fe","abstract_canon_sha256":"18bdfd91a6024757177c3ebb22924b10ef4d50e297150a58031487a64b0b8798"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:28.002418Z","signature_b64":"a/Wldvi2kBI81g0iIB4bEbZRzecPipAwgbrXVc8BO8Azq0X/D6bFRbuwGVfzwd7EJImaI/OsG0f9j/yJVoQoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8761e58df59d2be637472e9a426806ace9a21bae0d5b04344e3f3fbd6d36baab","last_reissued_at":"2026-05-18T00:30:28.001847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:28.001847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Local Nondeterminism of Spherical Fractional Brownian Motion","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xiaohong Lan, Yimin Xiao","submitted_at":"2017-07-17T07:13:49Z","abstract_excerpt":"Let $B = \\left\\{ B\\left( x\\right),\\, x\\in \\mathbb{S}^{2}\\right\\} $ be the fractional Brownian motion indexed by the unit sphere $\\mathbb{S}^{2}$ with index $0<H\\leq \\frac{1}{2}$, introduced by Istas \\cite{IstasECP05}. 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