{"paper":{"title":"Fluctuations of Ergodic Averages for Actions of Groups of Polynomial Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nikita Moriakov","submitted_at":"2016-08-17T18:08:52Z","abstract_excerpt":"It was shown by S. Kalikow and B. Weiss that, given a measure-preserving action of $\\mathbb{Z}^d$ on a probability space $X$ and a nonnegative measurable function $f$ on $X$, the probability that the sequence of ergodic averages $$ \\frac 1 {(2k+1)^d} \\sum\\limits_{g \\in [-k,\\dots,k]^d} f(g \\cdot x) $$ has at least $n$ fluctuations across an interval $(\\alpha,\\beta)$ can be bounded from above by $c_1 c_2^n$ for some universal constants $c_1 \\in \\mathbb{R}$ and $c_2 \\in (0,1)$, which depend only on $d,\\alpha,\\beta$. The purpose of this article is to generalize this result to measure-preserving ac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05033","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"}