{"paper":{"title":"Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Holland, Mike Todd","submitted_at":"2016-08-19T14:47:07Z","abstract_excerpt":"For a measure preserving dynamical system $(\\mathcal{X},f, \\mu)$, we consider the time series of maxima $M_n=\\max\\{X_1,\\ldots,X_n\\}$ associated to the process $X_n=\\phi(f^{n-1}(x))$ generated by the dynamical system for some observable $\\phi:\\mathcal{X}\\to\\mathbb{R}$. Using a point process approach we establish weak convergence of the process $Y_n(t)=a_n(M_{[nt]}-b_n)$ to an extremal process $Y(t)$ for suitable scaling constants $a_n,b_n\\in\\mathbb{R}$. Convergence here taking place in the Skorokhod space $\\mathbb{D}(0,\\infty)$ with the $J_1$ topology. We also establish distributional results f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05620","kind":"arxiv","version":2},"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"}