{"paper":{"title":"Return- and hitting-time distributions of small sets in infinite measure preserving systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Roland Zweim\\\"uller, Simon Rechberger","submitted_at":"2015-03-17T19:23:48Z","abstract_excerpt":"We study convergence of return- and hitting-time distributions of small sets $E_{k}$ with $\\mu(E_{k})\\rightarrow0$ in recurrent ergodic dynamical systems preserving an infinite measure $\\mu$. Some properties which are easy in finite measure situations break down in this null-recurrent setup. However, in the presence of a uniform set $Y$ with wandering rate regularly varying of index $1-\\alpha$ with $\\alpha\\in(0,1]$, there is a scaling function suitable for all subsets of $Y$. In this case, we show that return distributions for the $E_{k}$ converge iff the corresponding hitting time distributio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05175","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"}