{"paper":{"title":"Block-modified Wishart matrices and free Poisson laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ion Nechita, Teodor Banica","submitted_at":"2012-01-23T18:13:21Z","abstract_excerpt":"We study the random matrices of type $\\tilde{W}=(id\\otimes\\varphi)W$, where $W$ is a complex Wishart matrix of parameters $(dn,dm)$, and $\\varphi:M_n(\\mathbb C)\\to M_n(\\mathbb C)$ is a self-adjoint linear map. We prove that, under suitable assumptions, we have the $d\\to\\infty$ eigenvalue distribution formula $\\delta m\\tilde{W}\\sim\\pi_{mn\\rho}\\boxtimes\\nu$, where $\\rho$ is the law of $\\varphi$, viewed as a square matrix, $\\pi$ is the free Poisson law, $\\nu$ is the law of $D=\\varphi(1)$, and $\\delta=tr(D)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4792","kind":"arxiv","version":3},"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"}