{"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. 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)=\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4174","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}