{"paper":{"title":"On permutations of lacunary series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Christoph Aistleitner, Istvan Berkes, Robert Tichy","submitted_at":"2013-11-20T00:46:03Z","abstract_excerpt":"It is a well known fact that for periodic measurable $f$ and rapidly increasing $(n_k)_{k \\geq 1}$ the sequence $(f(n_kx))_{k\\ge 1}$ behaves like a sequence of independent, identically distributed random variables. For example, if $f$ is a periodic Lipschitz function, then $(f(2^kx))_{k\\ge 1}$ satisfies the central limit theorem, the law of the iterated logarithm and several further limit theorems for i.i.d.\\ random variables. Since an i.i.d.\\ sequence remains i.i.d.\\ after any permutation of its terms, it is natural to expect that the asymptotic properties of lacunary series are also permutat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4930","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"}