{"paper":{"title":"Group representations that resist random sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Alexander Russell, Cristopher Moore, Shachar Lovett","submitted_at":"2014-05-14T19:28:26Z","abstract_excerpt":"We show that there exists a family of groups $G_n$ and nontrivial irreducible representations $\\rho_n$ such that, for any constant $t$, the average of $\\rho_n$ over $t$ uniformly random elements $g_1, \\ldots, g_t \\in G_n$ has operator norm $1$ with probability approaching 1 as $n \\rightarrow \\infty$. More quantitatively, we show that there exist families of finite groups for which $\\Omega(\\log \\log |G|)$ random elements are required to bound the norm of a typical representation below $1$. This settles a conjecture of A. Wigderson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3636","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"}