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Unlike the previously investigated continuous time random walk model $\\overline{\\delta^2}$ converges to the ensemble average $<x^2 > \\sim t^{2 H}$ in the long measurement time limit. The convergence to ergodic behavior is however slow, and surprisingly the Hurst exponent $H=3/4$ marks the critical point of the speed of convergence. When $H<3/4$, the ergodicity breaking parameter ${EB} = {Var} ("},"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":"0809.2430","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.data-an","submitted_at":"2008-09-15T01:41:18Z","cross_cats_sorted":["astro-ph","cond-mat.stat-mech"],"title_canon_sha256":"80f6fa658e0060fc14c0df4019268416461a5f6aa7b49da1daece0cf0b388e41","abstract_canon_sha256":"6649cb03951db2c4931597f190597d399eb0735918525a1108024f2c95467c21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:50.118154Z","signature_b64":"FuiRxrMHioLDRriEcsrvyT+QqQSGqpO0A2L614rUvd94Hu771qg7rqAAnt4TRbE961h2XOJh2DwOpxGLIDohAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1535a50932f2e735e1824f93f4040c4f0c384dbb1ff669b285852b388348aa8a","last_reissued_at":"2026-05-18T03:00:50.117708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:50.117708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic Properties of Fractional Brownian-Langevin Motion","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["astro-ph","cond-mat.stat-mech"],"primary_cat":"physics.data-an","authors_text":"Eli Barkai, Weihua Deng","submitted_at":"2008-09-15T01:41:18Z","abstract_excerpt":"We investigate the time average mean square displacement $\\overline{\\delta^2}(x(t))=\\int_0^{t-\\Delta}[x(t^\\prime+\\Delta)-x(t^\\prime)]^2 dt^\\prime/(t-\\Delta)$ for fractional Brownian and Langevin motion. Unlike the previously investigated continuous time random walk model $\\overline{\\delta^2}$ converges to the ensemble average $<x^2 > \\sim t^{2 H}$ in the long measurement time limit. The convergence to ergodic behavior is however slow, and surprisingly the Hurst exponent $H=3/4$ marks the critical point of the speed of convergence. 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