{"paper":{"title":"Geometric Law for Multiple Returns until a Hazard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Ariel Rapaport, Yuri Kifer","submitted_at":"2018-02-21T10:33:19Z","abstract_excerpt":"For a $\\psi$-mixing stationary process $\\xi_0,\\xi_1,\\xi_2,...$ we consider the number $\\mathcal N_N$ of multiple recurrencies $\\{\\xi_{q_i(n)}\\in\\Gamma_N,\\, i=1,...,\\ell\\}$ to a set $\\Gamma_N$ for $n$ until the moment $\\tau_N$ (which we call a hazard) when another multiple recurrence $\\{\\xi_{q_i(n)}\\in\\Delta_N,\\, i=1,...,\\ell\\}$ takes place for the first time where $\\Gamma_N\\cap\\Delta_N= \\emptyset$ and $q_i(n)<q_{i+1}(n),\\, i=1,...,\\ell$ are nonnegative increasing functions taking on integer values on integers. It turns out that if $P\\{\\xi_0\\in\\Gamma_N\\}$ and $P\\{\\xi_0\\in\\Delta_N\\}$ decay in $N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07501","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"}