{"paper":{"title":"The Eigenvalue Point Process for Symmetric Group Permutation Representations on $k$-tuples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Benjamin Tsou","submitted_at":"2019-01-20T20:08:24Z","abstract_excerpt":"Equip the symmetric group $\\mathfrak{S}_n$ with the Ewens distribution. We study the eigenvalue point process of the permutation representation of $\\mathfrak{S}_n$ on $k$-tuples of distinct integers chosen from the set $\\{1,2,...,n\\}$. Taking $n \\to \\infty$, we find the limiting point process in the microscopic regime, i.e. when the eigenvalue point process is viewed at the scale of the mean eigenvalue spacing. A formula for the limiting eigenvalue gap probability in an interval is also given. In certain cases, a power series representation exists and a combinatorial procedure is given for com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06721","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"}