{"paper":{"title":"Anomalous time-scaling of extreme events in infinite systems and Birkhoff sums of infinite observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Mark Holland, Stefano Galatolo, Tomas Persson, Yiwei Zhang","submitted_at":"2018-10-25T07:16:37Z","abstract_excerpt":"We establish quantitative results for the statistical be\\-ha\\-vi\\-our of \\emph{infinite systems}. We consider two kinds of infinite system: i) a conservative dynamical system $(f,X,\\mu)$ preserving a $\\sigma$-finite measure $\\mu$ such that $\\mu(X)=\\infty$; ii) the case where $\\mu$ is a probability measure but we consider the statistical behaviour of an observable $\\phi\\colon X\\to[0,\\infty)$ which is non-integrable: $\\int \\phi \\, d\\mu=\\infty$.\n  In the first part of this work we study the behaviour of Birkhoff sums of systems of the kind ii). For certain weakly chaotic systems, we show that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10742","kind":"arxiv","version":3},"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"}