{"paper":{"title":"Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Charles Bordenave, Guillaume C\\'ebron, Mireille Capitaine, Serban Belinschi","submitted_at":"2019-06-25T17:24:47Z","abstract_excerpt":"We consider a square random matrix of size $N$ of the form $P(Y,A)$ where $P$ is a noncommutative polynomial, $A$ is a tuple of deterministic matrices converging in $\\ast$-distribution, when $N$ goes to infinity, towards a tuple $a$ in some $\\mathcal{C}^*$-probability space and $Y$ is a tuple of independent matrices with i.i.d. centered entries with variance $1/N$. We investigate the eigenvalues of $P(Y,A)$ outside the spectrum of $P(c,a)$ where $c$ is a circular system which is free from $a$. We provide a sufficient condition to guarantee that these eigenvalues coincide asymptotically with th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10674","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"}