{"paper":{"title":"Minimal growth harmonic functions on lamplighter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Ariel Yadin, Gady Kozma, Hugo Duminil-Copin, Itai Benjamini","submitted_at":"2016-07-04T07:16:10Z","abstract_excerpt":"We study the minimal possible growth of harmonic functions on lamplighters. We find that $(\\mathbb{Z}/2)\\wr \\mathbb{Z}$ has no sublinear harmonic functions, $(\\mathbb{Z}/2)\\wr \\mathbb{Z}^2$ has no sublogarithmic harmonic functions, and neither has the repeated wreath product $(\\dotsb(\\mathbb{Z}/2\\wr\\mathbb{Z}^2)\\wr\\mathbb{Z}^2)\\wr\\dotsb\\wr\\mathbb{Z}^2$. These results have implications on attempts to quantify the Derriennic-Kaimanovich-Vershik theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00753","kind":"arxiv","version":1},"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"}