{"paper":{"title":"Invariant random subgroups of linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Tsachik Gelander, Yair Glasner","submitted_at":"2014-07-10T17:33:40Z","abstract_excerpt":"Let $\\Gamma < \\mathrm{GL}_n(F)$ be a countable non-amenable linear group with a simple, center free Zariski closure, $\\mathrm{Sub}(\\Gamma)$ the space of all subgroups of $\\Gamma$ with the, compact, metric, Chabauty topology. An invariant random subgroup (IRS) of $\\Gamma$ is a conjugation invariant Borel probability measure on $\\mathrm{Sub}(\\Gamma)$. An $\\mathrm{IRS}$ is called nontrivial if it does not have an atom in the trivial group, i.e. if it is nontrivial almost surely. We denote by $\\mathrm{IRS}^{0}(\\Gamma)$ the collection of all nontrivial $\\mathrm{IRS}$ on $\\Gamma$.\n  We show that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2872","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"}