{"paper":{"title":"Limiting Spectral Distributions of Sums of Products of Non-Hermitian Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, H. K\\\"osters","submitted_at":"2015-06-14T20:45:18Z","abstract_excerpt":"For fixed $l,m \\ge 1$, let $\\mathbf{X}_n^{(0)},\\mathbf{X}_n^{(1)},\\dots,\\mathbf{X}_n^{(l)}$ be independent random $n \\times n$ matrices with independent entries, let $\\mathbf{F}_n^{(0)} := \\mathbf{X}_n^{(0)} (\\mathbf{X}_n^{(1)})^{-1} \\cdots (\\mathbf{X}_n^{(l)})^{-1}$, and let $\\mathbf{F}_n^{(1)},\\dots,\\mathbf{F}_n^{(m)}$ be independent random matrices of the same form as $\\mathbf{F}_n^{(0)}$. We investigate the limiting spectral distributions of the matrices $\\mathbf{F}_n^{(0)}$ and $\\mathbf{F}_n^{(1)} + \\dots + \\mathbf{F}_n^{(m)}$ as $n \\to \\infty$. Our main result shows that the sum $\\mathbf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04436","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"}