{"paper":{"title":"On the asymptotic behavior of weakly 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":"2013-12-03T00:39:27Z","abstract_excerpt":"Let $f$ be a measurable function satisfying $$f(x+1)=f(x), \\qquad \\int_0^1 f(x) dx=0, \\qquad \\textrm{Var} ~f < + \\infty,$$ and let $(n_k)_{k\\ge 1}$ be a sequence of integers satisfying $n_{k+1}/n_k \\ge q >1$ $(k=1, 2, \\ldots)$. By the classical theory of lacunary series, under suitable Diophantine conditions on $n_k$, $(f(n_kx))_{k\\ge 1}$ satisfies the central limit theorem and the law of the iterated logarithm. These results extend for a class of subexponentially growing sequences $(n_k)_{k\\ge 1}$ as well, but as Fukuyama (2009) showed, the behavior of $f(n_kx)$ is generally not permutation-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0668","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"}