{"paper":{"title":"Asymptotics of the Gelfand models of the symmetric groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Pierre-Lo\\\"ic M\\'eliot","submitted_at":"2010-09-21T10:28:43Z","abstract_excerpt":"If a partition $\\lambda$ of size n is chosen randomly according to the Plancherel measure $P_n[\\lambda] = (\\dim \\lambda)^2/n!$, then as n goes to infinity, the rescaled shape of $\\lambda$ is with high probability very close to a non-random continuous curve $\\Omega$ known as the Logan-Shepp-Kerov-Vershik curve. Moreover, the rescaled deviation of $\\lambda$ from this limit shape can be described by an explicit generalized gaussian process. In this paper, we investigate the analoguous problem when $\\lambda$ is chosen with probability proportional to $\\dim \\lambda$ instead of $(\\dim \\lambda)^2$. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4047","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"}