{"paper":{"title":"Model theory and metric convergence II: Averages of unitary polynomial actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.DS","authors_text":"Eduardo Due\\~nez, Jos\\'e N. Iovino","submitted_at":"2018-12-04T19:46:46Z","abstract_excerpt":"We use model theory of metric structures to prove the pointwise convergence, with a uniform metastability rate, of averages of a polynomial sequence $\\{T_n\\}$ (in Leibman's sense) of unitary transformations of a Hilbert space. As a special case, this applies to unitary sequences $\\{U^{p(n)}\\}$ where $p$ is a polynomial $\\mathbb{Z}\\to\\mathbb{Z}$ and $U$ a fixed unitary operator; however, our convergence results hold for arbitrary Leibman sequences. As a case study, we show that the non-nilpotent \"lamplighter group\" $\\mathbb{Z}\\wr\\mathbb{Z}$ is realized as the range of a suitable quadratic Leibm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01653","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"}