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More precisely, let $\\left(X,\\mathcal{B},m,T,\\alpha\\right)$ is a mixing, probability preserving Gibbs-Markov{\\normalsize{}. and let $\\varphi\\in L^{2}\\left(m\\right)$ be an aperiodic function with mean $0$. Set $S_{n}=\\sum_{k=0}^{n}X_{k}$ and define the hitting time process $L_{n}\\left(x\\right)$ be the number of times $S_{k}$ hits $x\\in\\mathbb {Z}$ up to step $n.$ The normalized local time process $l_{n}\\left(x\\right)$ is defined by $ l_{n}\\left(t\\right)=\\"},"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":"1406.4174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-16T21:19:27Z","cross_cats_sorted":[],"title_canon_sha256":"f0b285b17550edc3d1337e59b519f80d20fde77ea9b2d1c1a1cc61018ae64bad","abstract_canon_sha256":"59aca7823335a1623de4a16b6d5c7c2e91fb13750d6a5be1a4e19de54c1a9eee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:38.247924Z","signature_b64":"jZQIc2jvkM9STycvOMUir+kkB0XEdom5REkbXF0vcD6sSOVbsZjU195dmLg8gsOiR2PpHurCoYQYqL9iuhMxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f80f9df494296c31b0e90aad1b6dee8b414cc38744b9f04ca497abcc7a4c0e3d","last_reissued_at":"2026-05-18T02:49:38.247439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:38.247439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak invariance principle for the local times of Gibbs-Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michael Bromberg","submitted_at":"2014-06-16T21:19:27Z","abstract_excerpt":"The subject of this paper is to prove a functional weak invariance principle for the local time of a process generated by a Gibbs-Markov map. 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