{"paper":{"title":"Local spectral gap in simple Lie groups and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.GR","authors_text":"Adrian Ioana, Alireza Salehi Golsefidy, R\\'emi Boutonnet","submitted_at":"2015-03-22T20:31:54Z","abstract_excerpt":"We introduce a novel notion of {\\it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $\\Gamma\\curvearrowright G$, whenever $\\Gamma$ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group $G$. This extends to the non-compact setting recent works of Bourgain and Gamburd \\cite{BG06,BG10}, and Benoist and de Saxc\\'{e} \\cite{BdS14}. We present several applications to the Banach-Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06473","kind":"arxiv","version":3},"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"}