{"paper":{"title":"Compound Poisson statistics in conventional and nonconventional setups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Ariel Rapaport","submitted_at":"2014-04-14T09:48:50Z","abstract_excerpt":"Given a periodic point $\\omega$ in a $\\psi$-mixing shift with countable alphabet, the sequence $\\{S_{n}\\}$ of random variables counting the number of multiple returns to shrinking cylindrical neighborhoods of $\\omega$ is considered. Necessary and sufficient conditions for the convergence in distribution of $\\{S_{n}\\}$ are obtained, and it is shown that the limit is a Polya-Aeppli distribution. A global condition on the shift system, which guarantees the convergence in distribution of $\\{S_{n}\\}$ for every periodic point, is introduced. This condition is used to derive results for $f$-expansion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3516","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"}