{"paper":{"title":"Smallest eigenvalue distribution of the fixed trace Laguerre beta-ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dang-Zheng Liu, Da-Sheng Zhou, Yang Chen","submitted_at":"2010-02-21T15:30:36Z","abstract_excerpt":"In this paper we study entanglement of the reduced density matrix of a bipartite quantum system in a random pure state.\n  It transpires that this involves the computation of the smallest eigenvalue distribution of the fixed trace Laguerre ensemble of $N\\times N$ random matrices. We showed that for finite $N$ the smallest eigenvalue distribution may be expressed in terms of Jack polynomials.\n  Furthermore, based on the exact results, we found, a limiting distribution, when the smallest eigenvalue is suitably scaled with $N$ followed by a large $N$ limit. Our results turn out to be the same as t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3975","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"}