{"paper":{"title":"Asymptotic eigenvalue distributions of block-transposed Wishart matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","quant-ph"],"primary_cat":"math.PR","authors_text":"Ion Nechita, Teodor Banica","submitted_at":"2011-05-12T19:51:51Z","abstract_excerpt":"We study the partial transposition ${W}^\\Gamma=(\\mathrm{id}\\otimes \\mathrm{t})W\\in M_{dn}(\\mathbb C)$ of a Wishart matrix $W\\in M_{dn}(\\mathbb C)$ of parameters $(dn,dm)$. Our main result is that, with $d\\to\\infty$, the law of $m{W}^\\Gamma$ is a free difference of free Poisson laws of parameters $m(n\\pm 1)/2$. Motivated by questions in quantum information theory, we also derive necessary and sufficient conditions for these measures to be supported on the positive half line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2556","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"}