{"paper":{"title":"Fixed trace $\\beta$-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dang-Zheng Liu, Da-Sheng Zhou, Tao Qian","submitted_at":"2009-05-26T17:41:57Z","abstract_excerpt":"In the present paper, fixed trace $\\beta$-Hermite ensembles generalizing the fixed trace Gaussian Hermite ensemble are considered. For all $\\beta$, we prove the Wigner semicircle law for these ensembles by using two different methods: one is the moment equivalence method with the help of the matrix model for general $\\beta$, the other is to use asymptotic analysis tools. At the edge of the density, we prove that the edge scaling limit for $\\beta$-HE implies the same limit for fixed trace $\\beta$-Hermite ensembles. Consequently, explicit limit can be given for fixed trace GOE, GUE and GSE. Furt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4255","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"}